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 The test comprises of questions from all the sections of CAT exam i.e. Quantitative Aptitude, Verbal Ability, Reading Comprehension, Logical Reasoning and Data Interpretation.
 The duration of the test is 3 Hours and the total number of questions is 100.
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Question 1 of 100
1. Question
Category: Quantitative AptitudeQ1. A triangle ABC has 2 points marked on the side BC, 5 points marked on the side CA and 3 points marked on the side AB. None of these marked points is coincident with the vertices of the triangle ABC. All possible triangles are constructed taking any three of these points and the points A, B, C as the vertices. How many new triangles have atleast one vertex common with the triangle ABC?
Correct
Answer: Option (C)
Solution:
Total points including the vertices = 13 Out of these 13 points,
5 points on side AB (including B and A) are collinear
7 points on side AC (including C and A) are collinear
4 points on side BC (including B and C) are collinear
Thus, total triangles possible ^{13}c_{3} – ^{5}c_{3} – ^{7}c_{3} – ^{4}c_{3} = 237
Out of these, we should exclude those triangles which do not share the vertices A or B or C
Such triangles will be all the ones that can be formed with the points leaving out the vertices (10 such points).
Number of these triangles = ^{10}c_{3} – ^{3}c_{3} – ^{5}c_{3} = 120 (1+10) = 109
Where ^{10}c_{3} is the total number of triangles that can be formed with 3 points, ^{3}c_{3 is} the number that must be subtracted for the 3 collinear points lying on the side AB and ^{5}c_{3 }is the number that must be subtracted for the 5 collinear points lying on the side AC.
We should also exclude the triangle ABC itself. Hence the answer is 2371091 = 127.
Incorrect
Answer: Option (C)
Solution:
Total points including the vertices = 13 Out of these 13 points,
5 points on side AB (including B and A) are collinear
7 points on side AC (including C and A) are collinear
4 points on side BC (including B and C) are collinear
Thus, total triangles possible ^{13}c_{3} – ^{5}c_{3} – ^{7}c_{3} – ^{4}c_{3} = 237
Out of these, we should exclude those triangles which do not share the vertices A or B or C
Such triangles will be all the ones that can be formed with the points leaving out the vertices (10 such points).
Number of these triangles = ^{10}c_{3} – ^{3}c_{3} – ^{5}c_{3} = 120 (1+10) = 109
Where ^{10}c_{3} is the total number of triangles that can be formed with 3 points, ^{3}c_{3 is} the number that must be subtracted for the 3 collinear points lying on the side AB and ^{5}c_{3 }is the number that must be subtracted for the 5 collinear points lying on the side AC.
We should also exclude the triangle ABC itself. Hence the answer is 2371091 = 127.

Question 2 of 100
2. Question
Category: Quantitative AptitudeQ2. If a 3 digit number ‘abc’ has 3 factors, how many factors does the 6digit number ‘abcabc’ have?
Correct
Answer: Option (c)
Solution:
‘abc’ has exactly 3 factors, so ‘abc’ should be square of a prime number.
No. Of factors of a number (p^{a}q^{b}r^{c}) = (a+1)(b+1)(c+1)
‘abcabc’ = ‘abc’ × 1001
abcabc = abc × 7 × 11 × 13
‘abc’ has to be the square of a prime number.
It can either be 121 or 169 or it can be square of some other prime number.
When abc = 121 or 169, then ‘abcabc’ is of the form p^{3}q^{1}r^{1}.1, which should have 4 ×2 ×2=16 factors.
When ‘abc’ = square of any other prime number, then ‘abcabc’ is of the form p^{1}q^{1}r^{1}s^{2}, which should have 2× 2× 2× 3=24 factors.
So, ‘abcabc’ will either have 16 factors or 24 factors.
Incorrect
Answer: Option (c)
Solution:
‘abc’ has exactly 3 factors, so ‘abc’ should be square of a prime number.
No. Of factors of a number (p^{a}q^{b}r^{c}) = (a+1)(b+1)(c+1)
‘abcabc’ = ‘abc’ × 1001
abcabc = abc × 7 × 11 × 13
‘abc’ has to be the square of a prime number.
It can either be 121 or 169 or it can be square of some other prime number.
When abc = 121 or 169, then ‘abcabc’ is of the form p^{3}q^{1}r^{1}.1, which should have 4 ×2 ×2=16 factors.
When ‘abc’ = square of any other prime number, then ‘abcabc’ is of the form p^{1}q^{1}r^{1}s^{2}, which should have 2× 2× 2× 3=24 factors.
So, ‘abcabc’ will either have 16 factors or 24 factors.

Question 3 of 100
3. Question
Category: Quantitative AptitudeQ3. Vikalp, Nilay and Nilabh have visited a shop to buy LED TV and each one of them bought at least one unit of the TV. The shopkeeper gave a discount of 20% to Vikalp. Nilay, a good bargainer got two successive discounts of 20% and 60%. Nilabh, the hardest bargainer of all got three successive discounts of 20%, 40% and 50% respectively. After selling total of ‘x’ units to three of them, the shopkeeper calculated that he had given an overall discount of 56%. If 10 ≤x ≤20, then how many values of ‘x’ are possible? (Assume every one bought at least one unit).
Correct
Answer: Option (B)
Solution:
Discount to Nilay=1 .8× .4 = 68%
Discount to Nilabh = 1 .8× .6 ×.5 = 76%
Let a, b, c be the number of units sold to Vikalp, Nilay and Nilabh respectively.
So, .2a + .68 b + .76c = .56(a+b+c)
So, 5c = 3. ( 3ab),
So, c is multiple of 3
If, c=3 then (a,b) = (2,1) ,(3,4),(4,7)
If, c=6 then (a,b) = (4,2) ,(5,5) , (6,8)
Hence 6 solutions
Incorrect
Answer: Option (B)
Solution:
Discount to Nilay=1 .8× .4 = 68%
Discount to Nilabh = 1 .8× .6 ×.5 = 76%
Let a, b, c be the number of units sold to Vikalp, Nilay and Nilabh respectively.
So, .2a + .68 b + .76c = .56(a+b+c)
So, 5c = 3. ( 3ab),
So, c is multiple of 3
If, c=3 then (a,b) = (2,1) ,(3,4),(4,7)
If, c=6 then (a,b) = (4,2) ,(5,5) , (6,8)
Hence 6 solutions

Question 4 of 100
4. Question
Category: Quantitative AptitudeQ4. Taps to a tank are switched on in the following manner. Tap 1 for the first hour. Tap2 for the next two hrs and so on. The number indicated on each tap (1 for Tap number 1, 2 for tap number 2…) indicates its flow rate in litre/hr. These taps are filling a tank whose capacity is more than 1000litre. Moreover the capacity cannot be expressed as a difference of squares of two numbers. Find the tap no that fills the tank assuming that the tank’s capacity is minimum.
Correct
Answer: Option (d)
Solution:
The smallest number possible is 1002 (this is a 4k+2 number, it cannot be expressed as difference of squares) .
Therefore our equation becomes. 1*1 + 2*2+…. N*n= 1002. N= 13.93.
i.e. when the 14^{th} tap is open the tank gets filled.
Incorrect
Answer: Option (d)
Solution:
The smallest number possible is 1002 (this is a 4k+2 number, it cannot be expressed as difference of squares) .
Therefore our equation becomes. 1*1 + 2*2+…. N*n= 1002. N= 13.93.
i.e. when the 14^{th} tap is open the tank gets filled.

Question 5 of 100
5. Question
Category: Quantitative AptitudeQ5. Let g(x)= x+1. The number of values that ‘x’ can take (given that its range is between
2 and 2 (both inclusive)) for which g(x3), g(x1), g(x+1) are in AP is?Correct
Answer: Option (b)
Solution:
g(x3) = x2
g(x1)=x
g(x+1)= x+2
these will be in AP if
2x = x2+x+2
If x<2, 2x= (x2)(x+2) or 2x= 2x. hence x<2
Similarly for 2≤ x< 0, we get 2x= (x2)+(x+2) =>x=2
For 0≤ x< 2, 2x= (x2)+(x+2) => x=2
Also, for x≥2, 2x= x2+x+2 => 2x=2x
Therefore x= 2 and x=2 satisfy the equation.
Incorrect
Answer: Option (b)
Solution:
g(x3) = x2
g(x1)=x
g(x+1)= x+2
these will be in AP if
2x = x2+x+2
If x<2, 2x= (x2)(x+2) or 2x= 2x. hence x<2
Similarly for 2≤ x< 0, we get 2x= (x2)+(x+2) =>x=2
For 0≤ x< 2, 2x= (x2)+(x+2) => x=2
Also, for x≥2, 2x= x2+x+2 => 2x=2x
Therefore x= 2 and x=2 satisfy the equation.

Question 6 of 100
6. Question
Category: Quantitative AptitudeQ6. Find the remainder when 7^{55} is divided by 29.
Correct
Answer: Option (b)
Solution:
g(x3) = x2
g(x1)=x
g(x+1)= x+2
these will be in AP if
2x = x2+x+2
If x<2, 2x= (x2)(x+2) or 2x= 2x. hence x<2
Similarly for 2≤ x< 0, we get 2x= (x2)+(x+2) =>x=2
For 0≤ x< 2, 2x= (x2)+(x+2) => x=2
Also, for x≥2, 2x= x2+x+2 => 2x=2x
Therefore x= 2 and x=2 satisfy the equation.
Incorrect
Answer: Option (b)
Solution:
g(x3) = x2
g(x1)=x
g(x+1)= x+2
these will be in AP if
2x = x2+x+2
If x<2, 2x= (x2)(x+2) or 2x= 2x. hence x<2
Similarly for 2≤ x< 0, we get 2x= (x2)+(x+2) =>x=2
For 0≤ x< 2, 2x= (x2)+(x+2) => x=2
Also, for x≥2, 2x= x2+x+2 => 2x=2x
Therefore x= 2 and x=2 satisfy the equation.

Question 7 of 100
7. Question
Category: Quantitative AptitudeQ7. A 50m long platoon is marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m. How much distance (approximately) did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.
Correct
Answer: Option (a)
Solution:
The last person covered 120.71 meters.
It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered – while person moving forward and backward – are equal. Let’s assume that when the last person reached the first person, the platoon moved X meters forward.
Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.
Similarly, while moving back the last person moved [50(50X)] = X meters whereas the platoon moved (50X) meters.
Now, as the ratios are equal,
(50+X)/X = X/(50X)
(50+X)*(50X) = X*X
Solving, X=35.355 meters
Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters
=120 m (approximately).
Incorrect
Answer: Option (a)
Solution:
The last person covered 120.71 meters.
It is given that the platoon and the last person moved with uniform speed. Also, they both moved for the identical amount of time. Hence, the ratio of the distance they covered – while person moving forward and backward – are equal. Let’s assume that when the last person reached the first person, the platoon moved X meters forward.
Thus, while moving forward the last person moved (50+X) meters whereas the platoon moved X meters.
Similarly, while moving back the last person moved [50(50X)] = X meters whereas the platoon moved (50X) meters.
Now, as the ratios are equal,
(50+X)/X = X/(50X)
(50+X)*(50X) = X*X
Solving, X=35.355 meters
Thus, total distance covered by the last person
= (50+X) + X
= 2*X + 50
= 2*(35.355) + 50
= 120.71 meters
=120 m (approximately).

Question 8 of 100
8. Question
Category: Quantitative AptitudeQ8. The integers from 1 to 1000 are written in order around a circle. Starting at 1, every fifteenth number is marked (that is 1, 16, 31, etc.). This process is continued until a number is reached which has already been marked. How many unmarked numbers remain?
Correct
Answer: Option (d)
Solution:
Consider the first round: – All the numbers which leave a remainder of 1 when divided by 15 will be marked. (1, 16, 31, 46 … 991)
Consider the second round: – The first number to be marked is 991 + 15 – 1000 = 6. Thereafter all the numbers which leave a remainder 6 when divided by 15 will be marked. (6, 21, 36, 51 … 996)
Consider the third round: – The first number to be marked is 996 + 15 – 1000 = 11. And all the numbers which leave a remainder 11 when divided by 11 will be marked. (11, 26, 41, 56 … 986)
The first number to be marked in the fourth round is 986 + 15 – 1000 = 1. Now the cycle will repeat.
If we see the numbers which are getting marked are: 1, 6, 11, 16, 21, 26, 31, 36 … 996
i.e. all the numbers which divided by 5 leave a remainder 1. So there are 1000/5 = 200 numbers, so 1000 – 200 = 800 numbers remain unmarked.
Incorrect
Answer: Option (d)
Solution:
Consider the first round: – All the numbers which leave a remainder of 1 when divided by 15 will be marked. (1, 16, 31, 46 … 991)
Consider the second round: – The first number to be marked is 991 + 15 – 1000 = 6. Thereafter all the numbers which leave a remainder 6 when divided by 15 will be marked. (6, 21, 36, 51 … 996)
Consider the third round: – The first number to be marked is 996 + 15 – 1000 = 11. And all the numbers which leave a remainder 11 when divided by 11 will be marked. (11, 26, 41, 56 … 986)
The first number to be marked in the fourth round is 986 + 15 – 1000 = 1. Now the cycle will repeat.
If we see the numbers which are getting marked are: 1, 6, 11, 16, 21, 26, 31, 36 … 996
i.e. all the numbers which divided by 5 leave a remainder 1. So there are 1000/5 = 200 numbers, so 1000 – 200 = 800 numbers remain unmarked.

Question 9 of 100
9. Question
Category: Quantitative AptitudeQ9. In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50paisa, 25paisa and 10 paisa coin?
Correct
Answer: Option (b)
Solution:
Suppose we take x 50paisa coins, y 25paisa coins and z 10paisa coins.
We have x + y + z = 85 and 50x + 25y + 10z = 1875, because x, y and z are all integers, z should be a multiple of 5.
Possible values are
x y z
2 63 20
5 55 25
8 47 30
…
…
23 7 55
So there are eight solutions.
You should notice here that an increase of 5 in z and 3 in x and decrease of 8 in y neither changes the number of coins nor the value.
Incorrect
Answer: Option (b)
Solution:
Suppose we take x 50paisa coins, y 25paisa coins and z 10paisa coins.
We have x + y + z = 85 and 50x + 25y + 10z = 1875, because x, y and z are all integers, z should be a multiple of 5.
Possible values are
x y z
2 63 20
5 55 25
8 47 30
…
…
23 7 55
So there are eight solutions.
You should notice here that an increase of 5 in z and 3 in x and decrease of 8 in y neither changes the number of coins nor the value.

Question 10 of 100
10. Question
Category: Quantitative AptitudeQ10. Find the complete range of values of x that satisfies  x + 3  >x^{2} 11x +30
Correct
Answer: Option (d)
Solution :
Conventional Approach
Given inequality is
We consider 2 cases
Case (i) x> 3
Ix + 3I = x+3
x+3 >x^{2}11x+30 =>x^{2}12x+27<0 (x9) (x3)<0 \(x\varepsilon \left ( 3,9 \right )\)
Case(ii) x <3 Ix +3I = x 3 x3 >x^{2}11x+30
=>x^{2}– 10x + 33 < 0=>x^{2}– 10x + 25 +8 < 0 = (x5)^{2}+ 8 <0
(x5)^{2}+8 is always a positive quantity, irrespective of the value of x. Hence we do not have any value for x in this interval. Hence the valid interval for x is (3, 9).
Shortcut Elimination Approach
Step 1 Choose a value for x which is present in 2 answer options and absent in the other 2. Eg) x=4 satisfies the range specified in option (a) and (d), but does not form a part of the range in option (b) and (c)
At x=4
LHS= 4+3=7
RHS= 1644+30= 2. LHS>RHS. It is satisfied. This means that answer options, which do not include x=4 can be directly eliminated as they can NEVER be the right answer
Step 2 Choose a value for x which is there in one of the remaining 2 options and absent in the other
Eg) take x=10. This option satisfies the range in option (a) but is absent in option (d)
At x=10
LHS= 10+3=13
RHS= 100110+30= 20
LHS <RHS. This violates the condition in the question. This means that option (a) can never be the right answer.
Thus, by elimination, answer is option (d).
Incorrect
Answer: Option (d)
Solution :
Conventional Approach
Given inequality is
We consider 2 cases
Case (i) x> 3
Ix + 3I = x+3
x+3 >x^{2}11x+30 =>x^{2}12x+27<0 (x9) (x3)<0 \(x\varepsilon \left ( 3,9 \right )\)
Case(ii) x <3 Ix +3I = x 3 x3 >x^{2}11x+30
=>x^{2}– 10x + 33 < 0=>x^{2}– 10x + 25 +8 < 0 = (x5)^{2}+ 8 <0
(x5)^{2}+8 is always a positive quantity, irrespective of the value of x. Hence we do not have any value for x in this interval. Hence the valid interval for x is (3, 9).
Shortcut Elimination Approach
Step 1 Choose a value for x which is present in 2 answer options and absent in the other 2. Eg) x=4 satisfies the range specified in option (a) and (d), but does not form a part of the range in option (b) and (c)
At x=4
LHS= 4+3=7
RHS= 1644+30= 2. LHS>RHS. It is satisfied. This means that answer options, which do not include x=4 can be directly eliminated as they can NEVER be the right answer
Step 2 Choose a value for x which is there in one of the remaining 2 options and absent in the other
Eg) take x=10. This option satisfies the range in option (a) but is absent in option (d)
At x=10
LHS= 10+3=13
RHS= 100110+30= 20
LHS <RHS. This violates the condition in the question. This means that option (a) can never be the right answer.
Thus, by elimination, answer is option (d).

Question 11 of 100
11. Question
Category: Quantitative AptitudeQ11. Consider the non decreasing sequence of positive integers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5…. in which nth positive number appears n times. Find the remainder when the 2000th term is divided by 4.
Correct
Answer: Option (d)
Solution:
Let us see the sequence of the numbers:
Number Last term of the number
1 1
2 3
3 6
4 10
_ _
N \(\frac{N\left ( N+1 \right )}{2}\)
We have to find the value of N for the 2000th term.
If N = 62, the last term that ends with N is (1/2* 62 * 63) = 1953.
Therefore, the next 63 terms are 63. So the 2000th term is 63. So the remainder is 3.
Incorrect
Answer: Option (d)
Solution:
Let us see the sequence of the numbers:
Number Last term of the number
1 1
2 3
3 6
4 10
_ _
N \(\frac{N\left ( N+1 \right )}{2}\)
We have to find the value of N for the 2000th term.
If N = 62, the last term that ends with N is (1/2* 62 * 63) = 1953.
Therefore, the next 63 terms are 63. So the 2000th term is 63. So the remainder is 3.

Question 12 of 100
12. Question
Category: Quantitative AptitudeQ12. Three distinct prime numbers less than 10 are taken and all the numbers are formed by arranging all the digits taken. Now the difference between the largest and the smallest number is 495. It is also given that the sum of the digits is more than 13, what is the product of the digits?
Correct
Answer: Option (b)
Solution:
Prime numbers less than 10 = 2,3,5,7
If the difference between the largest and the smallest number is 5, the prime numbers in the end position have to be 7 and 2
The smallest and largest numbers are of the form 2 x 7 & 7 x 2. Since it is given that the sum of the digits is >13, X can only be 5.
Verifying 752257 = 495. Answer is option (b)
Incorrect
Answer: Option (b)
Solution:
Prime numbers less than 10 = 2,3,5,7
If the difference between the largest and the smallest number is 5, the prime numbers in the end position have to be 7 and 2
The smallest and largest numbers are of the form 2 x 7 & 7 x 2. Since it is given that the sum of the digits is >13, X can only be 5.
Verifying 752257 = 495. Answer is option (b)

Question 13 of 100
13. Question
Category: Quantitative AptitudeQ13. PQR is a right angled triangle with PQ=8, QR=6, QT as altitude. If a circle is drawn with QT as diameter, what is the area of the shaded region?
Correct
Answer: Option (c)
Solution :
Let PT=x, Then 8^{2}x^{2} = 6^{2} – (10x)^{2}; => x = 6.4
Thus QT = 8^{2} – 6.4^{2} = 4.8; ST=4.8/√2;
Area of square STUQ = \(\left ( \frac{4.8}{\sqrt{2}}\right )^{2}\);
Area of circle: π (2.4)^{2};
Area of shaded region: ½ (π (2.4)^{2}– );
Incorrect
Answer: Option (c)
Solution :
Let PT=x, Then 8^{2}x^{2} = 6^{2} – (10x)^{2}; => x = 6.4
Thus QT = 8^{2} – 6.4^{2} = 4.8; ST=4.8/√2;
Area of square STUQ = \(\left ( \frac{4.8}{\sqrt{2}}\right )^{2}\);
Area of circle: π (2.4)^{2};
Area of shaded region: ½ (π (2.4)^{2}– );

Question 14 of 100
14. Question
Category: Quantitative AptitudeQ14. Amar, Akbar and Anthony ran on a racetrack, with Amar finishing 160 m ahead of Akbar and 400 m ahead of Anthony. Akbar finished the race 300 m ahead of Anthony. The three of them ran the entire distance with their respective constant speeds. What was the length of the racetrack?
Correct
Answer: Option (b)
Solution:
Using the concept of ratios of speed (speed directly proportional to distance), we can easily arrive at the total distance. The images below give a picture of the distances when Amar and Akbar finish the race
Length of the race track = 400 +x
The ratio of Akbar and Anthony’s speed can be arrived at as (240+x)/x=(400+x)/(100+x)
Now go from answer options, answer will be option (b) 800 m
Verifying, x = 400
640/400=800/500. Thus, answer is option (b)
Incorrect
Answer: Option (b)
Solution:
Using the concept of ratios of speed (speed directly proportional to distance), we can easily arrive at the total distance. The images below give a picture of the distances when Amar and Akbar finish the race
Length of the race track = 400 +x
The ratio of Akbar and Anthony’s speed can be arrived at as (240+x)/x=(400+x)/(100+x)
Now go from answer options, answer will be option (b) 800 m
Verifying, x = 400
640/400=800/500. Thus, answer is option (b)

Question 15 of 100
15. Question
Category: Quantitative AptitudeQ15. How many pairs of positive integers, x, y exist; such that x^{2} + 3y and ^{y2} + 3x are both perfect squares.
Correct
Answer: Option (d)
Solution:
Since x and y are positive, we may write
x^{2} + 3y = (x + a)^{2}, and
y^{2} + 3x = (y + b)^{2}Where a, b are positive integers.
Expanding, we find that the squared terms cancel, leaving the linear simultaneous equations
3y = 2ax + a^{2}
3x = 2by + b^{2}Solving, we obtain
x = \(x=\frac{2a^{2}b+3b^{2}}{94ab}\)
y = \(y=\frac{2b^{a}+3a^{2}}{94ab}\)Since a and b are positive, the numerator in each fraction will be positive. For the denominator to be positive, we must have ab = 1 or 2.
If (a,b) = (1,1), (1,2), (2,1), then, respectively, (x,y) = (1,1), (16,11), (11,16). Hence these are the only solutions.
Incorrect
Answer: Option (d)
Solution:
Since x and y are positive, we may write
x^{2} + 3y = (x + a)^{2}, and
y^{2} + 3x = (y + b)^{2}Where a, b are positive integers.
Expanding, we find that the squared terms cancel, leaving the linear simultaneous equations
3y = 2ax + a^{2}
3x = 2by + b^{2}Solving, we obtain
x = \(x=\frac{2a^{2}b+3b^{2}}{94ab}\)
y = \(y=\frac{2b^{a}+3a^{2}}{94ab}\)Since a and b are positive, the numerator in each fraction will be positive. For the denominator to be positive, we must have ab = 1 or 2.
If (a,b) = (1,1), (1,2), (2,1), then, respectively, (x,y) = (1,1), (16,11), (11,16). Hence these are the only solutions.

Question 16 of 100
16. Question
Category: Quantitative AptitudeQ16. How many ordered pairs (ab,cd) be formed that satisfy the property ab^{2} + cd^{2}= ba^{2} + dc^{2} where ab^{2} represents square of a 2 digit number ab ?
Correct
Answer: Option (a)
Solution:
(10a+b)^{2} + (10c+d)^{2} = (10b + a)^{2} + (10d+c)^{2}
→ a^{2} + c^{2} = b^{2} + d^{2}
The condition is satisfied when (ab, cd) = (14,87) , (15,75) , (17,84) , (26,97) , (27,96)
Each pair of numbers can occur in 4 different ways as ab is different from ba.
Therefore, number of ordered pairs (ab,cd) = 5*4 = 20
Alternate Approach:
This is a property of square mirrors. There are 5 such possibilities of 2 digit numbers. The number of ordered pairs (ab,cd) = 4*5 = 20 [(ab,cd), (ba,dc), (cd,ab), (dc,ba)]
Incorrect
Answer: Option (a)
Solution:
(10a+b)^{2} + (10c+d)^{2} = (10b + a)^{2} + (10d+c)^{2}
→ a^{2} + c^{2} = b^{2} + d^{2}
The condition is satisfied when (ab, cd) = (14,87) , (15,75) , (17,84) , (26,97) , (27,96)
Each pair of numbers can occur in 4 different ways as ab is different from ba.
Therefore, number of ordered pairs (ab,cd) = 5*4 = 20
Alternate Approach:
This is a property of square mirrors. There are 5 such possibilities of 2 digit numbers. The number of ordered pairs (ab,cd) = 4*5 = 20 [(ab,cd), (ba,dc), (cd,ab), (dc,ba)]

Question 17 of 100
17. Question
Category: Quantitative AptitudeQ17. A certain clock marks every hour by striking a number of times equal to the hour and the time required for a stroke is exactly equal to the time interval between strokes. At 9:00 a.m. the time lapse between the beginning of the first stroke and the end of the last stroke is 34 seconds. At 18:00 hrs. how many seconds elapse between the beginning of the first stroke and the end of the last stroke:
Correct
Answer: Option (d)
Solution:
At 9:00 a.m. there are 9 strokes and 8 intervals between strokes.
Thus for 17 equal time intervals, Time = 34 sec.
For 1 interval time = 2 seconds. At 18:00 hours i.e. (6:00 p.m.) there are 6 strokes and 5 intervals i.e. total 11 time intervals of 2 seconds.
Answer = 22 seconds.Incorrect
Answer: Option (d)
Solution:
At 9:00 a.m. there are 9 strokes and 8 intervals between strokes.
Thus for 17 equal time intervals, Time = 34 sec.
For 1 interval time = 2 seconds. At 18:00 hours i.e. (6:00 p.m.) there are 6 strokes and 5 intervals i.e. total 11 time intervals of 2 seconds.
Answer = 22 seconds. 
Question 18 of 100
18. Question
Category: Quantitative AptitudeQ18. L and M make an appointment to meet on 20th Nov. 2005 at the CAT examination centre, but without fixing anything other than that the appointment is between 10 a.m. to 11 a.m. They decide to wait no longer than 10 minutes for each other. Assuming that each is independently likely to arrive at any time during the hour, find the probability that they will meet
Correct
Answer: Option (c)
Solution:
We can consider the entire time to be represented by the xy plot: where on the x axis we represent the time of one of them coming and on the y axis the other person coming.
L&M will meet provided xy<=10
(x, y) lies on or inside thesquare with vertices 0(0, 0) A(60, 0) B(60, 60) and C (0, 60).
The region that lying inside the square OABC and satisfying the inequality .x – y > 0 consists two triangles DAE and GFC.
Sum of areas of two triangle = (50)^{2 }+ (50)^{2}=(50)^{2}
Probability =1 =1 = \(=\frac{1}{2}\left ( 50 \right )^{2}+\frac{1}{2}\left ( 50 \right )^{2}=\left ( 50 \right )^{2}\)
Incorrect
Answer: Option (c)
Solution:
We can consider the entire time to be represented by the xy plot: where on the x axis we represent the time of one of them coming and on the y axis the other person coming.
L&M will meet provided xy<=10
(x, y) lies on or inside thesquare with vertices 0(0, 0) A(60, 0) B(60, 60) and C (0, 60).
The region that lying inside the square OABC and satisfying the inequality .x – y > 0 consists two triangles DAE and GFC.
Sum of areas of two triangle = (50)^{2 }+ (50)^{2}=(50)^{2}
Probability =1 =1 = \(=\frac{1}{2}\left ( 50 \right )^{2}+\frac{1}{2}\left ( 50 \right )^{2}=\left ( 50 \right )^{2}\)

Question 19 of 100
19. Question
Category: Quantitative AptitudeQ19. What is the maximum number of points of intersection of 10 squares of same side length? (Assume no two edges overlap)
Correct
Answer: Option (c)
Solution:
Number of ways of selecting two squares from 10 squares= ^{10}C_{2}.
Each pair of squares can meet at maximum of 8 points.
If there are no common points of intersection, maximum number of intersections=^{10}C_{2}×8=360Incorrect
Answer: Option (c)
Solution:
Number of ways of selecting two squares from 10 squares= ^{10}C_{2}.
Each pair of squares can meet at maximum of 8 points.
If there are no common points of intersection, maximum number of intersections=^{10}C_{2}×8=360 
Question 20 of 100
20. Question
Category: Quantitative AptitudeQ20. In the figure shown below, all the vertical lines are parallel to each other & are equally spaced. All the horizontal lines are parallel to each other and are equally spaced. What fraction of the area of ABCD, is shaded?
Correct
Answer: Option (C)
Solution:
The image can be redrawn as follows, by joining all the points
Thus, there are 24 unit squares. The number of unit squares shaded = 6. Required ratio = \(=\frac{6}{24}=\frac{1}{4}\)
Incorrect
Answer: Option (C)
Solution:
The image can be redrawn as follows, by joining all the points
Thus, there are 24 unit squares. The number of unit squares shaded = 6. Required ratio = \(=\frac{6}{24}=\frac{1}{4}\)

Question 21 of 100
21. Question
Category: Quantitative AptitudeQ21. ABC is an equilateral triangle and AX, BY and CZ are three parallel lines. Find the area of triangle ABC.
Correct
Answer: Option (b)
Solution:
There is no constraint given, other than that ABC is an equilateral triangle and AX∥BY∥CZ.
We can therefore assume that X,Y and Z are points on the side AC itself. If we assume the equilateral triangle to have a side=2, and the Y is the mid point of AC, then AY=YB=1
Area of the triangle = \(=\frac{\sqrt{3}}{4}\left ( a+b \right )^{2}=\sqrt{3}\)
Look in the answer options and eliminate those options where you do not get √3 on substituting a=1 and b=1.
Incorrect
Answer: Option (b)
Solution:
There is no constraint given, other than that ABC is an equilateral triangle and AX∥BY∥CZ.
We can therefore assume that X,Y and Z are points on the side AC itself. If we assume the equilateral triangle to have a side=2, and the Y is the mid point of AC, then AY=YB=1
Area of the triangle = \(=\frac{\sqrt{3}}{4}\left ( a+b \right )^{2}=\sqrt{3}\)
Look in the answer options and eliminate those options where you do not get √3 on substituting a=1 and b=1.

Question 22 of 100
22. Question
Category: Quantitative AptitudeQ22. There are 13 couples, 5 single men and 7 single women in party. Every man shakes hand with every woman once. But none shakes hand with his wife. How many handshakes in total took place in the party?
Correct
Answer: Option (d)
There are 13 couples: 13 men & 13 women In addition to it, there are 5 single men and 7 single women. Now, 5 single men can shake hands with 20 women, therefore 5*20 = 100 ways. Also, each of 13 males (from the couples) can shake hands with 12 women (except his wife) + 7 single women. So, 13 19 = 247 ways. Therefore, in total 347 ways.
Incorrect
Answer: Option (d)
There are 13 couples: 13 men & 13 women In addition to it, there are 5 single men and 7 single women. Now, 5 single men can shake hands with 20 women, therefore 5*20 = 100 ways. Also, each of 13 males (from the couples) can shake hands with 12 women (except his wife) + 7 single women. So, 13 19 = 247 ways. Therefore, in total 347 ways.

Question 23 of 100
23. Question
Category: Quantitative AptitudeQ23. Ken is the best sugar cube retailer in the nation. Trevor, who loves sugar, is coming over to make an order. Ken knows Trevor cannot afford more than 127 sugar cubes, but might ask for any number of cubes less than or equal to that. Ken has to prepare ‘n‘cups of cubes, where ‘n’ is as small as possible, with which he can satisfy any order Trevor might make. How many cubes are in the cup with the most sugar?
Correct
Answer: Option (b)
This question is entirely based on the powers of 2 less than 127.
Thus the answer is 2^{6}= 64 cubes in the cup with the most sugar.
How is that? Let us look at this important concept using the unitary approach
Take the number 5.
The question in other words how many numbers would you need so that all the numbers from 1 to 5 are possible using addition.
The powers of 2 less than 5 are 2^{0} = 1, 2^{1}=2 and 2^{2}=4
1= 1
2= 2
3= 1+2
4=4
5=4+1
Thus, we see that with powers of 2 we can easily write all the numbers below the highest power of 2 taken.
In case we take up to 2^{2},then we can write all values upto 2^{3}– 1or 7.
2^{0} = 1
2^{1}=2
2^{1} + 2^{0} =3
2^{2}=4
2^{2}+2^{0} =5
2^{2}+2^{1}=6
2^{2}+2^{1}+2^{0} = 7
Hence with 3 numbers you can write upto 7.
Hence to add up to 127 you will have to consider the powers of 2 till 2^{6}.
So the cups must contain 1, 2, 4, 8, 16, 32, and 64 cubes of sugar,with 64 being the most number of cubes in one cup.
Incorrect
Answer: Option (b)
This question is entirely based on the powers of 2 less than 127.
Thus the answer is 2^{6}= 64 cubes in the cup with the most sugar.
How is that? Let us look at this important concept using the unitary approach
Take the number 5.
The question in other words how many numbers would you need so that all the numbers from 1 to 5 are possible using addition.
The powers of 2 less than 5 are 2^{0} = 1, 2^{1}=2 and 2^{2}=4
1= 1
2= 2
3= 1+2
4=4
5=4+1
Thus, we see that with powers of 2 we can easily write all the numbers below the highest power of 2 taken.
In case we take up to 2^{2},then we can write all values upto 2^{3}– 1or 7.
2^{0} = 1
2^{1}=2
2^{1} + 2^{0} =3
2^{2}=4
2^{2}+2^{0} =5
2^{2}+2^{1}=6
2^{2}+2^{1}+2^{0} = 7
Hence with 3 numbers you can write upto 7.
Hence to add up to 127 you will have to consider the powers of 2 till 2^{6}.
So the cups must contain 1, 2, 4, 8, 16, 32, and 64 cubes of sugar,with 64 being the most number of cubes in one cup.

Question 24 of 100
24. Question
Category: Quantitative AptitudeQ24. Each corner of a square subtends an angle of 30⁰ at the top of a tower ‘h’ meters high standing in the centre of the square. If ‘a’ is the length of the each side of square then
Correct
Answer: Option (c)
We can go ahead and assume values for h and deduce the value of a, substitute it in the given equations and eliminate the wrong answer choices.
Let us assume the value of h=\(\sqrt[]3\)
As it is a 306090 triangle we will have the sides in the ratio as 1: \(\sqrt[]3\) :2
Hence the diagonal of the square will be 2, the height of tower ‘h’ will be \(\sqrt[]3\)and the side ‘a’ will be \(\sqrt[]2\).
Now applying this in the answer options we see that only option (c)gives us RHS= LHS.
Hence option (c) is correct.
Incorrect
Answer: Option (c)
We can go ahead and assume values for h and deduce the value of a, substitute it in the given equations and eliminate the wrong answer choices.
Let us assume the value of h=\(\sqrt[]3\)
As it is a 306090 triangle we will have the sides in the ratio as 1: \(\sqrt[]3\) :2
Hence the diagonal of the square will be 2, the height of tower ‘h’ will be \(\sqrt[]3\)and the side ‘a’ will be \(\sqrt[]2\).
Now applying this in the answer options we see that only option (c)gives us RHS= LHS.
Hence option (c) is correct.

Question 25 of 100
25. Question
Category: Quantitative AptitudeQ25. Find the approximate value of x, for this equation to be satisfied:
\(x^{x^{x^{x^{x}}}}2=o\)
Correct
Answer: Option (a)
Go from answer options.
If x= 1.41 = \(\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}}}\) =\(2^{^{\frac{1}{2}2^{\frac{1}{2}}}}\) = \(2^{1^{1^{1}}}\) = 2 2 =0. Hence the equation is satisfied.
Incorrect
Answer: Option (a)
Go from answer options.
If x= 1.41 = \(\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}}}}}\) =\(2^{^{\frac{1}{2}2^{\frac{1}{2}}}}\) = \(2^{1^{1^{1}}}\) = 2 2 =0. Hence the equation is satisfied.

Question 26 of 100
26. Question
Category: Quantitative AptitudeQ26. For the given equation \(x^{9} + 5x^{8} – x^{3} + 7x + 3 = 0\), how many maximum real roots are possible?
Correct
Solution: let f(x) = \(x^{9} + 5x^{8} – x^{3} + 7x + 3 = 0\)
We can solve this question easily using Descartes’ Rule
According to Descartes’ rule maximum number of positive real roots = number of sign
Changes in f(x) = 2
Similarly, Maximum number of negative real roots = number of sign changes in f (x)
Note: To find f (x) replace “x” by “x” in each instance
∴f (x) = \(– x^{9} + 5x^{8} + x^{3} – 7x + 3 = 0\)
Maximum number of negative real roots = number of sign changes in f (x) = 3
Zero cannot be a root because constant part is also involved in equation.
So maximum number of real roots = 2 + 3 = 5.
Incorrect
Solution: let f(x) = \(x^{9} + 5x^{8} – x^{3} + 7x + 3 = 0\)
We can solve this question easily using Descartes’ Rule
According to Descartes’ rule maximum number of positive real roots = number of sign
Changes in f(x) = 2
Similarly, Maximum number of negative real roots = number of sign changes in f (x)
Note: To find f (x) replace “x” by “x” in each instance
∴f (x) = \(– x^{9} + 5x^{8} + x^{3} – 7x + 3 = 0\)
Maximum number of negative real roots = number of sign changes in f (x) = 3
Zero cannot be a root because constant part is also involved in equation.
So maximum number of real roots = 2 + 3 = 5.

Question 27 of 100
27. Question
Category: Quantitative AptitudeQ27. The total amount of money spent on the purchase of pencils, rubbers and pens is Rs. 45. The cost of one pencil, one rubber and two pens is Rs. 2, Rs. 3 and Rs. 4 respectively. The total number of pencils bought is greater and less than the number of pens and the number of rubbers bought respectively. How many different combinations of the number of pencils, rubbers and pens bought are possible?
Correct
Answer: (c)
Solution:
Let x, y and z be the number of pencils, rubbers and pens bought. The cost of one pencil, one rubber and one pen is Rs.2, Rs.3 and Rs.4 respectively.
Now, 2x + 3y + 4z = 45.
Therefore, \(x=\frac{453y4z}{2}\)
Also, \(Z<\frac{453y4z}{2}>Y\)
Or, 6z + 3y < 45 and 5y + 4z > 45.
Possible values of y and z that satisfy the above equation is (7, 3); (9, 2) and (11, 1) in that order. Therefore, there are 3 different possible combinations.
Incorrect
Answer: (c)
Solution:
Let x, y and z be the number of pencils, rubbers and pens bought. The cost of one pencil, one rubber and one pen is Rs.2, Rs.3 and Rs.4 respectively.
Now, 2x + 3y + 4z = 45.
Therefore, \(x=\frac{453y4z}{2}\)
Also, \(Z<\frac{453y4z}{2}>Y\)
Or, 6z + 3y < 45 and 5y + 4z > 45.
Possible values of y and z that satisfy the above equation is (7, 3); (9, 2) and (11, 1) in that order. Therefore, there are 3 different possible combinations.

Question 28 of 100
28. Question
Category: Quantitative AptitudeQ28. A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than
Correct
Answer: Option (b)
Solution:
Let the number of correct answers be ‘x’, number of wrong answers be ‘y’ and number of questions not attempted be ‘z’.
Thus, x + y + z = 50 … (i)
\(X\frac{Y}{3}\frac{Z}{6}=32\)
and
The second equation can be written as,
6x – 2y – z = 192 … (ii)
Adding the two equations we get,
7x – y = 242 →\(7xy=242\rightarrow x=\frac{242+y}{7}\)
Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can have is 3. Hence option (b).
Alternatively go from answer options.
Choose a multiple of 3. A score of 32 can be obtained with “3” wrong attempts itself. Hence it is the minimum.
Incorrect
Answer: Option (b)
Solution:
Let the number of correct answers be ‘x’, number of wrong answers be ‘y’ and number of questions not attempted be ‘z’.
Thus, x + y + z = 50 … (i)
\(X\frac{Y}{3}\frac{Z}{6}=32\)
and
The second equation can be written as,
6x – 2y – z = 192 … (ii)
Adding the two equations we get,
7x – y = 242 →\(7xy=242\rightarrow x=\frac{242+y}{7}\)
Since, x and y are both integers, y cannot be 1 or 2. The minimum value that y can have is 3. Hence option (b).
Alternatively go from answer options.
Choose a multiple of 3. A score of 32 can be obtained with “3” wrong attempts itself. Hence it is the minimum.

Question 29 of 100
29. Question
Category: Quantitative AptitudeQ29. How many pairs of positive integers (a, b) are there such that ‘a’ and ‘b’ have no common factor greater than 1 and a/b +14b/9a is an integer?
Correct
Answer: Option (d)
Let u =\(\frac{a}{b}\) . Then the problem is equivalent to finding all possible rational numbers ‘u’ such that
u+ \(\frac{14}{9u}\) K, for some integer K.
This equation is equivalent to 9u^{2}9uk+14=0
9u^{2}9uk+14=0 whose solutions are,
\(u=\frac{9k\pm \sqrt{81k^{2}504}}{18}\)
\(=\frac{k}{2}\pm \frac{1}{6}\sqrt{9k^{2}56}\)Hence u is rational if and only if –
\(\sqrt{9k^{2}56}\) is rational, which is true if and only if 9k^{2 }56 is a perfect square. Suppose that 9k^{2}56 =s^{2 }for some positive integer S.
(3k+s) (3ks) =56
The only factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56. So, (3ks) and (3k+s) is one of the ordered pairs (1, 56), (2, 28), (4, 14) and (7, 8). The cases (1, 56) and (7, 8) yield no integral solutions. The cases (2,28) and (4, 14) yield k=5 and k=3 respectively.
If k=5 then u=\(\frac{1}{3}\) or u=\(\frac{14}{3}\)
If k=3 then u=\(\frac{2}{3}\) or u= \(\frac{7}{3}\) .
Therefore there are four pairs (a,b) that satisfy the given conditions, namely (1, 3), (2, 3), (7, 3) and (14, 3).
Incorrect
Answer: Option (d)
Let u =\(\frac{a}{b}\) . Then the problem is equivalent to finding all possible rational numbers ‘u’ such that
u+ \(\frac{14}{9u}\) K, for some integer K.
This equation is equivalent to 9u^{2}9uk+14=0
9u^{2}9uk+14=0 whose solutions are,
\(u=\frac{9k\pm \sqrt{81k^{2}504}}{18}\)
\(=\frac{k}{2}\pm \frac{1}{6}\sqrt{9k^{2}56}\)Hence u is rational if and only if –
\(\sqrt{9k^{2}56}\) is rational, which is true if and only if 9k^{2 }56 is a perfect square. Suppose that 9k^{2}56 =s^{2 }for some positive integer S.
(3k+s) (3ks) =56
The only factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56. So, (3ks) and (3k+s) is one of the ordered pairs (1, 56), (2, 28), (4, 14) and (7, 8). The cases (1, 56) and (7, 8) yield no integral solutions. The cases (2,28) and (4, 14) yield k=5 and k=3 respectively.
If k=5 then u=\(\frac{1}{3}\) or u=\(\frac{14}{3}\)
If k=3 then u=\(\frac{2}{3}\) or u= \(\frac{7}{3}\) .
Therefore there are four pairs (a,b) that satisfy the given conditions, namely (1, 3), (2, 3), (7, 3) and (14, 3).

Question 30 of 100
30. Question
Category: Quantitative AptitudeQ30. The quadratic function f(x) = ax2 + bx + c is known to pass through the points (1, 6); (7, 6), and (1, – 6). Find the smallest value of the function.
Correct
Answer: Option (b)
Solution:
If the points (1, 6), (7, 6), and (1, 6) lie on the graph of y = ax^{2} + bx + c, then 6 = a – b + c, 6 = 49a + 7b + c, 6 =a + b + c. Solving this system, we get a =1, b = – 6, c = – 1. The graph of f(x)= x^{2} – 6x – 1 is a parabola that opens upward and the vertex is \(\left ( \frac{b}{1},\frac{D}{4a}\right)=\left ( 3,10 \right )\) = (3, 10).
Incorrect
Answer: Option (b)
Solution:
If the points (1, 6), (7, 6), and (1, 6) lie on the graph of y = ax^{2} + bx + c, then 6 = a – b + c, 6 = 49a + 7b + c, 6 =a + b + c. Solving this system, we get a =1, b = – 6, c = – 1. The graph of f(x)= x^{2} – 6x – 1 is a parabola that opens upward and the vertex is \(\left ( \frac{b}{1},\frac{D}{4a}\right)=\left ( 3,10 \right )\) = (3, 10).

Question 31 of 100
31. Question
Category: Quantitative AptitudeQ31. There are 2 stations A and B, between them there are 9 intermediate stations. A train starts from station A and it stops at 4 intermediate stations such that not more than 2 stations are consecutive. What is the number of such possible cases?
Correct
Answer: Option (b)
Solution:
Case 1(The train stops at no consecutive station)
Let us remove the stations at which train stops, so (94=5) stations are left
i.e. _ _ _ _ _ , between these 5 stations there are 6 gaps and the train stops at
these gaps. Hence the number of ways is ^{6}C_{4} = 15 Ways
Case 2(The train stops at 1 consecutive station and 2 nonconsecutive stations)
So, we will have 2 stations in 1 gap and 2 stations in 2 gaps. Also, there are 3 possible ways in which this can happen (2 1 1, 1 1 2, 1 2 1).
Hence possible number of ways is = 3*(^{6}C_{3}) = 60 Ways
Case 3 (The train stops at 2 consecutive stations)
So, we will have 2 stations in 1 gap and 2 stations in 1 more gap.
Total number of ways = ^{6}C_{2}= 15 Ways
Total number of ways = 15+60+15 = 90.
Incorrect
Answer: Option (b)
Solution:
Case 1(The train stops at no consecutive station)
Let us remove the stations at which train stops, so (94=5) stations are left
i.e. _ _ _ _ _ , between these 5 stations there are 6 gaps and the train stops at
these gaps. Hence the number of ways is ^{6}C_{4} = 15 Ways
Case 2(The train stops at 1 consecutive station and 2 nonconsecutive stations)
So, we will have 2 stations in 1 gap and 2 stations in 2 gaps. Also, there are 3 possible ways in which this can happen (2 1 1, 1 1 2, 1 2 1).
Hence possible number of ways is = 3*(^{6}C_{3}) = 60 Ways
Case 3 (The train stops at 2 consecutive stations)
So, we will have 2 stations in 1 gap and 2 stations in 1 more gap.
Total number of ways = ^{6}C_{2}= 15 Ways
Total number of ways = 15+60+15 = 90.

Question 32 of 100
32. Question
Category: Quantitative AptitudeQ32. Tiles are packed into packets of 6, 9 and 50.What is the largest number of tiles that cannot be purchased with any combination of above packets? (Tiles cannot be sold loose)
Correct
Answer: Option (c)
Solution:
After 6 all multiples of 3 would be covered. After 50+6 all 3x+2 would be covered. After 50+50+6 all 3x+1 would be covered. So for 106 and above all tile combinations are possible. Now below 106, 105 is possible (3x format) and 104 is also possible (3x+2). So, the largest possible value which can’t be obtained will be 103.
Incorrect
Answer: Option (c)
Solution:
After 6 all multiples of 3 would be covered. After 50+6 all 3x+2 would be covered. After 50+50+6 all 3x+1 would be covered. So for 106 and above all tile combinations are possible. Now below 106, 105 is possible (3x format) and 104 is also possible (3x+2). So, the largest possible value which can’t be obtained will be 103.

Question 33 of 100
33. Question
Category: Quantitative AptitudeQ33. If x, y, z are positive numbers such that \(x + [y] + {z} = 3.8, [x] + {y} + z = 3.2, {x} + y + [z] = 2.2,\) where [p] denotes the greatest integer less than or equal to p and {p} denotes the fractional part of p, e.g. [1.23] = 1, {1.23} = 23/100. The numerical value of \([x^{2} + y^{2} + z^{2}]\) is
part of p, e.g. [1.23] = 1, . The numerical value of [x 2 + y 2 + z 2 ] is
Correct
Answer: Option (c)
Solution:
Adding the three equations we get, 2(x + y + z) = 9.2 => x + y + z = 4.6.
Subtracting first eq. from the above eq. we get {y} + [z] = 0.8 => {y} = 0.8 and [z] = 0.
Subtracting second eq. from the above eq. {x} + [y] = 1.4 => {x} = 0.4 and [y] = 1.
Subtracting third eq. from the above eq. [x] + {z} = 2.4 => [x] = 2, and {z} = 0.4 => x = 2.4, y = 1.8 and z = 0.4. Hence, choice (c) is the right answer.
Incorrect
Answer: Option (c)
Solution:
Adding the three equations we get, 2(x + y + z) = 9.2 => x + y + z = 4.6.
Subtracting first eq. from the above eq. we get {y} + [z] = 0.8 => {y} = 0.8 and [z] = 0.
Subtracting second eq. from the above eq. {x} + [y] = 1.4 => {x} = 0.4 and [y] = 1.
Subtracting third eq. from the above eq. [x] + {z} = 2.4 => [x] = 2, and {z} = 0.4 => x = 2.4, y = 1.8 and z = 0.4. Hence, choice (c) is the right answer.

Question 34 of 100
34. Question
Category: Quantitative AptitudeQ34. A sum of money compounded annually triples itself in 3 years. After how many years the sum becomes 27 times of itself?
Correct
Answer: Option (b)
Solution:
Solution: From 1^{st} condition \(3x=x\left ( 1+\frac{r}{100} \right )^{3}\)
So, \(\left ( 1+\frac{r}{100} \right )=3^{\frac{1}{3}}\).
From 2^{nd} condition – Now, 27x = x
Þ\(27x=x\left ( 1+\frac{r}{100} \right )^{t}\)
Incorrect
Answer: Option (b)
Solution:
Solution: From 1^{st} condition \(3x=x\left ( 1+\frac{r}{100} \right )^{3}\)
So, \(\left ( 1+\frac{r}{100} \right )=3^{\frac{1}{3}}\).
From 2^{nd} condition – Now, 27x = x
Þ\(27x=x\left ( 1+\frac{r}{100} \right )^{t}\)

Question 35 of 100
35. Question
Category: Reading ComprehensionPassage 1
Directions for Q.35 to Q.39 – Read the following passage and answer the questions that follow.
Moral philosophy, or the science of human nature, may be treated after two different manners; each of which has its peculiar merit, and may contribute to the entertainment, instruction, and reformation of mankind. The one considers man chiefly as born for action; and as influenced in his measures by taste and sentiment; pursuing one object, and avoiding another, according to the value which these objects seem to possess, and according to the light in which they present themselves. As virtue, of all objects, is allowed to be the most valuable, this species of philosophers paint her in the most amiable colours; borrowing all helps from poetry and eloquence, and treating their subject in an easy and obvious manner, and such as is best fitted to please the imagination, and engage the affections. They select the most striking observations and instances from common life; place opposite characters in a proper contrast; and alluring us into the paths of virtue by the views of glory and happiness, direct our steps in these paths by the soundest precepts and most illustrious examples. They make us feel the difference between vice and virtue; they excite and regulate our sentiments; and so they can but bend our hearts to the love of probity and true honour, they think, that they have fully attained the end of all their labors.
The other species of philosophers consider man in the light of a reasonable rather than an active being, and endeavour to form his understanding more than cultivate his manners. They regard human nature as a subject of speculation; and with a narrow scrutiny examine it, in order to find those principles, which regulate our understanding, excite our sentiments, and make us approve or blame any particular object, action, or behaviour. They think it a reproach to all literature, that philosophy should not yet have fixed, beyond controversy, the foundation of morals, reasoning, and criticism; and should forever talk of truth and falsehood, vice and virtue, beauty and deformity, without being able to determine the source of these distinctions. While they attempt this arduous task, they are deterred by no difficulties; but proceeding from particular instances to general principles, they still push on their enquiries to principles more general, and rest not satisfied till they arrive at those original principles, by which, in every science, all human curiosity must be bounded. Though their speculations seem abstract and even unintelligible to common readers, they aim at the approbation of the learned and the wise; and think themselves sufficiently compensated for the labour of their whole lives, if they can discover some hidden truths, which may contribute to the instruction of posterity.
It is certain that the easy and obvious philosophy will always, with the generality of mankind, have the preference above the accurate and abstruse; and by many will be recommended, not only as more agreeable, but more useful than the other. It enters more into common life; moulds the heart and affections; and, by touching those principles which actuate men, reforms their conduct, and brings them nearer to that model of perfection which it describes. On the contrary, the abstruse philosophy, being founded on a turn of mind, which cannot enter into business and action, vanishes when the philosopher leaves the shade, and comes into open day; nor can its principles easily retain any influence over our conduct and behaviour. The feelings of our heart, the agitation of our passions, the vehemence of our affections, dissipate all its conclusions, and reduce the profound philosopher to a mere plebeian.
This also must be confessed, that the most durable, as well as justest fame, has been acquired by the easy philosophy, and that abstract reasoners seem hitherto to have enjoyed only a momentary reputation, from the caprice or ignorance of their own age, but have not been able to support their renown with more equitable posterity. It is easy for a profound philosopher to commit a mistake in his subtle reasonings; and one mistake is the necessary parent of another, while he pushes on his consequences, and is not deterred from embracing any conclusion, by its unusual appearance, or its contradiction to popular opinion. But a philosopher, who purposes only to represent the common sense of mankind in more beautiful and more engaging colours, if by accident he falls into error, goes no farther; but renewing his appeal to common sense, and the natural sentiments of the mind, returns into the right path, and secures himself from any dangerous illusions. The fame of Cicero flourishes at present; but that of Aristotle is utterly decayed. La Bruyere passes the seas, and still maintains his reputation: But the glory of Malebranche is confined to his own nation, and to his own age. And Addison, perhaps, will be read with pleasure, when Locke shall be entirely forgotten.
Q.35. What is the central idea of this passage?
Correct
Soln: A.
The statement in option B is a general statement that the author makes to introduce the topic but it is not the main theme of the passage. The author does not go into detail to compare the merits and demerits of these two ways. Option C is true but is again not the main theme. Option D and E are neither mentioned in or can be inferred from the passage.
Option A is the main theme of the passage. The author highlights it in the opening line of the third paragraph where he writes that ‘It is certain that the easy and obvious philosophy will always, with the generality of mankind, have the preference above the accurate and abstruse…..’ and goes on further to elaborate this point.Incorrect
Soln: A.
The statement in option B is a general statement that the author makes to introduce the topic but it is not the main theme of the passage. The author does not go into detail to compare the merits and demerits of these two ways. Option C is true but is again not the main theme. Option D and E are neither mentioned in or can be inferred from the passage.
Option A is the main theme of the passage. The author highlights it in the opening line of the third paragraph where he writes that ‘It is certain that the easy and obvious philosophy will always, with the generality of mankind, have the preference above the accurate and abstruse…..’ and goes on further to elaborate this point. 
Question 36 of 100
36. Question
Category: Reading ComprehensionQ.36. What can be inferred about abstruse philosophers from the passage?
Correct
Soln. C
Option A is only partially true. While the abstruse philosophers do attempt the understand the origins of human behavior, they do not entirely refrain from cultivating the manners of the masses. See the first line of paragraph 2 ‘endeavour to form his understanding more than cultivate his manners.’ Option B is out of the scope of the passage as there is no discussion on the development of philosophical thought. Option D seems to be deviously close but carefully observe what the author says in the last paragraph. He mentions that abstruse philosophers have been famous in their times but their fame has waned since then. So one cannot make a sweeping statement that ‘they have never been able to attain fame of the same magnitude as that of obvious philosophers’. Option E suggests that abstruse thinkers suffered ignominy due to their erroneous reasoning. This is not suggested anywhere in the passage.The first line of the second passage contains the phrase ‘in order to find those principles’. So the abstruse philosophers must first believe that there exist some basic laws that govern human nature before attempting to find them.
Incorrect
Soln. C
Option A is only partially true. While the abstruse philosophers do attempt the understand the origins of human behavior, they do not entirely refrain from cultivating the manners of the masses. See the first line of paragraph 2 ‘endeavour to form his understanding more than cultivate his manners.’ Option B is out of the scope of the passage as there is no discussion on the development of philosophical thought. Option D seems to be deviously close but carefully observe what the author says in the last paragraph. He mentions that abstruse philosophers have been famous in their times but their fame has waned since then. So one cannot make a sweeping statement that ‘they have never been able to attain fame of the same magnitude as that of obvious philosophers’. Option E suggests that abstruse thinkers suffered ignominy due to their erroneous reasoning. This is not suggested anywhere in the passage.The first line of the second passage contains the phrase ‘in order to find those principles’. So the abstruse philosophers must first believe that there exist some basic laws that govern human nature before attempting to find them.

Question 37 of 100
37. Question
Category: Reading ComprehensionQ.37. Which of the following best describes the relation of the third paragraph to the passage a whole?
Correct
Soln. C
The third paragraph explains the central idea of the passage that people find obvious philosophy more appealing than abstruse philosophy.
It neither presents a new argument nor offers a summary of earlier ideas. The author offers examples to provide evidence for his main idea and not for a general point in the last line of the last paragraph.Incorrect
Soln. C
The third paragraph explains the central idea of the passage that people find obvious philosophy more appealing than abstruse philosophy.
It neither presents a new argument nor offers a summary of earlier ideas. The author offers examples to provide evidence for his main idea and not for a general point in the last line of the last paragraph. 
Question 38 of 100
38. Question
Category: Reading ComprehensionQ.38. In the final paragraph, why does the author refer to the posterity as more “equitable”?
Correct
Soln. D
Option A suggests that the posterity will be inherently more just than the previous generation. This is nowhere stated nor can be inferred from the passage. Also, ‘equitable’ here is not in the sense of justness but more in the sense of being knowledgeable. Options B and C may look plausible but on close observation of the last paragraph: ‘that abstract reasoners seem hitherto to have enjoyed only a momentary reputation, from the caprice or ignorance of their own age, ‘ it is apparent that people of the abstruse philosopher’s time may have regarded him with positivity due to the prevalent ignorance or caprice. However it does not say anything about why the next generation should be more equitable. Option E is partially correct as it states that the posterity will be more knowledgeable but the reasoning it gives for that is not supported by the passage. We do not know whether that happened due to new philosophical thoughts coming into picture.
Option D suggests that the posterity will have the advantage of getting to know the philosopher’s thoughts both in theory and in practice, compare them and judge him for his philosophical accuracy. In this regard, they will be more knowledgeable or equitable.Incorrect
Soln. D
Option A suggests that the posterity will be inherently more just than the previous generation. This is nowhere stated nor can be inferred from the passage. Also, ‘equitable’ here is not in the sense of justness but more in the sense of being knowledgeable. Options B and C may look plausible but on close observation of the last paragraph: ‘that abstract reasoners seem hitherto to have enjoyed only a momentary reputation, from the caprice or ignorance of their own age, ‘ it is apparent that people of the abstruse philosopher’s time may have regarded him with positivity due to the prevalent ignorance or caprice. However it does not say anything about why the next generation should be more equitable. Option E is partially correct as it states that the posterity will be more knowledgeable but the reasoning it gives for that is not supported by the passage. We do not know whether that happened due to new philosophical thoughts coming into picture.
Option D suggests that the posterity will have the advantage of getting to know the philosopher’s thoughts both in theory and in practice, compare them and judge him for his philosophical accuracy. In this regard, they will be more knowledgeable or equitable. 
Question 39 of 100
39. Question
Category: Reading ComprehensionQ.39. Which of the following best describes the attitude of the author towards abstruse philosophers in the passage?
Correct
Soln. B
It is necessary here to note that the author is not criticizing the abstruse philosophers. He is merely stating that their philosophy is not as popular with people as obvious philosophy is. The author is neither pro nor against abstruse philosophers. He is just looking at abstruse philosophy from the point of view of the masses and saying that it does not give them something concrete to relate to. So, his view towards the philosophers is dispassionately objective.Incorrect
Soln. B
It is necessary here to note that the author is not criticizing the abstruse philosophers. He is merely stating that their philosophy is not as popular with people as obvious philosophy is. The author is neither pro nor against abstruse philosophers. He is just looking at abstruse philosophy from the point of view of the masses and saying that it does not give them something concrete to relate to. So, his view towards the philosophers is dispassionately objective. 
Question 40 of 100
40. Question
Category: Reading ComprehensionPassage 2
Directions for Q.40 to Q.42 – Read the following passage and answer the questions that follow.
For years, behavioral scientists have been telling us that they have a great deal to contribute to decision theory and management. Their work most applicable to business, however, was often overshadowed by that of economists. But as the assumptions of rational behavior and “perfect information” that formed the basis of much of the work in economics concerning markets came into question, behavioral science not based on those assumptions gained ascendance. At first, the contributions from behavioral science were based on laboratory tests, too many of them involving handy college students. They helped describe biases (at least among those being tested). For example, we learned that people tend to devalue longterm returns in relation to shortterm gains. They tend not to buy and sell according to selfset rules. A person willing to pay up to $200 for a ticket to a sporting event is not, once he owns it, willing to sell it at any price above $200—counter to what economists would predict. Behavioral science regards it as perfectly reasonable behavior, explained by what they call the “endowment effect.” It is one of many behaviors that help explain why markets are not always “rational,” why they may not be a reflection of perfect information, why people buy high and sell low.
Brain scanning technology adds a new dimension to this work. It has provided fodder for books on a variety of subjects, all of which rely to some degree on brain reaction to stimuli. By introducing various stimuli while scanning a person’s brain, we can begin to learn which parts govern how we feel, how we respond to stimuli, and how we react to challenges.
A recent study of “midlife northeast American adults” raises questions about whether we are entering the next stage in what might be termed an era of neuromanagement. In it, a group of researchers claim to have found that brain structure and the density of cells in the right posterior parietal cortex are associated with willingness to take risks. They found that participants with higher gray matter volume in this region exhibited less risk aversion. The results “identify what might be considered the first stable biomarker for financial riskattitude,” according to the authors.The study is a distant cousin to those that have located the side of the brain associated with creativity and the portion of the brain that is stimulated, for example, by gambling or music. Assuming: (1) there will be more research efforts combining the results of brain scans with behavioral exercises, and (2) findings are proven to be more valid than, say, those associated with phrenology, it raises some interesting questions about the future. Is it possible that some organizations selecting and hiring talent may, in the future, require a brain scan, just as some require psychological testing today? Is hiring on the basis of brain structure much different than hiring, for example, on the basis of height or other characteristics required to perform certain jobs? Or does it raise too many ethical questions? For example, who will own the data? How will it be used? How would we apply the results?
Q.40. According to the passage, brain scanning technology can reveal all of the following regions of person’s brain EXCEPT the regions that:
Correct
Soln. C
In the second paragraph,while the author mentions that brain scans can help isolate the parts that govern how we react to challenges, he does not say whether the responses are rational or not. The parts of the brain that determine a person’s financial risk appetite and those that are activated while he’s gambling have been identified by researchers. So A and B cannot be the answer choices.
Incorrect
Soln. C
In the second paragraph,while the author mentions that brain scans can help isolate the parts that govern how we react to challenges, he does not say whether the responses are rational or not. The parts of the brain that determine a person’s financial risk appetite and those that are activated while he’s gambling have been identified by researchers. So A and B cannot be the answer choices.

Question 41 of 100
41. Question
Category: Reading ComprehensionQ.41. According to the passage, which of the following behaviours of people are better explained by behavioural science than by economics?
Correct
Soln. E
In the first paragraph, the author mentions that the findings of behaviour science suggest that people ‘ devalue long term returns as compared to short term gains’. We also find an explanation of why ‘people buy high and sell low’. The endowment effect is just the opposite of what is suggested by Option C. Economics and not behaviour science will say that people will sell their $ 200 ticket for $ 205.
Incorrect
Soln. E
In the first paragraph, the author mentions that the findings of behaviour science suggest that people ‘ devalue long term returns as compared to short term gains’. We also find an explanation of why ‘people buy high and sell low’. The endowment effect is just the opposite of what is suggested by Option C. Economics and not behaviour science will say that people will sell their $ 200 ticket for $ 205.

Question 42 of 100
42. Question
Category: Reading ComprehensionQ.42. What could be a suitable title to this passage?
Correct
Soln. D
The passage is basically about how developments in science are furthering an era where behaviour science and brain imaging could join hands to determine the behaviour of people. Such a development will pose questions like the ones mentioned in the last paragraph. All the other titles address a part of the passage but do not touch upon the central idea of ‘neuromanagement’.Incorrect
Soln. D
The passage is basically about how developments in science are furthering an era where behaviour science and brain imaging could join hands to determine the behaviour of people. Such a development will pose questions like the ones mentioned in the last paragraph. All the other titles address a part of the passage but do not touch upon the central idea of ‘neuromanagement’. 
Question 43 of 100
43. Question
Category: Reading ComprehensionPassage 3
Directions for Q.43 to Q.47 – Read the following passage and answer the questions that follow.
Kant uses the word ‘noumena’ to refer to things in themselves, which he describes as ‘intelligible existences’ which ‘are not objects of our senses’. Kant is on difficult territory with his notion of noumena. To begin with, given that we can know nothing about them, in what way does it make any sense to talk about them existing? By Kant’s own standard, is it not the case that noumena are devoid of any meaning? Kant argues that although we cannot have any conception of what noumena are, we can nevertheless have a representation of them. But he goes on to state that this representation is a ‘limitative conception’. That is, that noumenal representations simply mark the limit of human understanding and that is their necessary function. Unfortunately, this response does not say a great deal about noumena: it does not givethem a positive meaning.
The characteristics that Kant placed on noumena leads ultimately to the question of how we can justify a belief in them. Kant argued that they must exist because phenomena are appearances, thus they must be appearances of something, and that something must be noumena. But surely we are not justified in calling them appearances a priori. We may have a conception of them as appearances empirically, in that we say that suchandsuch a phenomena is the appearance of suchandsuch an object, but as we have seen the notion of phenomena and of object is accommodated within Kant’s model of cognition, and thus appearance is a relation between them. There is no essential property of phenomena which make them appearances. Ultimately, Kant’s noumena are unknowable and, as Russell pointed out, ‘the “thinginitself” was an awkward element in Kant’s philosophy, and was abandoned by his immediate successors’.
The important point here is that in the same way we can be sceptical about the existence of external reality within the empiricist framework, and thus be led down the path of Berkeley’s idealism and solipsism, so we can be sceptical about the existence of noumena within the Kantian framework and we can be led to a similarly solipsistic position. Given that we have seen that Kant defends himself against the charge of idealism, it is worth returning back to that argument more critically.
Kant’s refutation of idealism is based on the insight that what we take to be the outside world is immediately given. The real world that we live in is immediately revealed by our intuitions, and we make sense of that world through our conceptions. Kant wrote that idealism ‘assumed, that the only immediate experience is internal, and that from this we can only infer the existence of external things… But our proof shows that external experience is properly immediate’. Hence, because the external world is immediately given, there is no justification in being sceptical about it.
The difficulty with Kant’s refutation is not so much with the refutation itself, but with what he is defending. The external world, in the Kantian framework, is ultimately the construct of our faculties of mind (this being the thesis of transcendental ideality). It is built upon the intuitions of sensibility, and the conceptions of the understanding. Given this foundation, it is interesting to speculate what the situation would be if I lacked these faculties. No doubt I would cease to exist as a human consciousness, but would it also follow that the external world would also not exist. It is difficult to see how Kant could avoid this conclusion. Thus, Kant’s refutation works so long as I am alive and am able to think about the existence of an external world, yet becomes difficult if I speculate on the consequences of my own nonexistence.
Thus it follows that the external world is not objective in the sense that it exists independently of the thinking subject. As has been argued earlier, Kant does describe the external world as objective. However, what is meant by ‘objective’, for Kant, is that we hold a certain relation with the external world, whereby we conceive ourselves as subjects within an independent framework of objects (i.e. as explained earlier, regardless of how I happen to be looking at a chair, the nature of the chair remains fixed and independent of my perspective). This relational objectivity does not necessary imply an ontological objectivity. Kant can defend his view of the external world against idealism, so long as he frames the charge of idealism at the relational qualities of objectivity.
Kant was aware that the external world was limited by our understanding, and noumena are introduced partly as proof of this (i.e. noumena are the limits of human understanding). It is the noumena that play the role of independent existences beyond the thinking subject. They have ontological objectivity (in contrast, for Kant we do not stand in any relation to them, as the very notion of a relation cannot be applied to them). As such it is noumena that Kant needs to defend against charges of idealism, in addition to empirical reality. As they are ‘unknowable’, it is difficult to know how this defence can be made.
If noumena are taken away from Kant’s theory, or are doubted, then everything I understand, including all objects, places and other people, become mere characters within my active mind. The world can only be appreciated as independently existing within the noumenal theory.Q.43. Why is the author very critical regarding Kant’s theory of Noumena?
Correct
Soln. (b)
The last line of the third paragraph “Given that we have seen that Kant defends himself against the charge of idealism, it is worth returning back to that argument more critically.”
Also the fifth Paragraph states that “The external world, in the Kantian framework, is ultimately the construct of our faculties of mind”
So adding these two lines leads to option b
The author himself states why he is critical about Kant’s arguments in the above lines. All the other options correspond to his contemplations and the author doesn’t link them to critical argument (which the whole passage is all about).Incorrect
Soln. (b)
The last line of the third paragraph “Given that we have seen that Kant defends himself against the charge of idealism, it is worth returning back to that argument more critically.”
Also the fifth Paragraph states that “The external world, in the Kantian framework, is ultimately the construct of our faculties of mind”
So adding these two lines leads to option b
The author himself states why he is critical about Kant’s arguments in the above lines. All the other options correspond to his contemplations and the author doesn’t link them to critical argument (which the whole passage is all about). 
Question 44 of 100
44. Question
Category: Reading ComprehensionQ.44. Which of the following are Kant’s views on Noumena?
A) Noumena are the limits of human understanding
B) Noumena does not have a positive meaning
C) Noumena must exist
D) Noumena has Ontological objectivityCorrect
Soln. (a)
b) and d) are the authors view on noumena and not Kant’s.Incorrect
Soln. (a)
b) and d) are the authors view on noumena and not Kant’s. 
Question 45 of 100
45. Question
Category: Reading ComprehensionQ.45. According to the passage, which of the following conclusion would be refuted by the Kants defence against Idealism?
Correct
Soln. (d)
Fifth paragraph last line gives the clue to this question.
“Thus, Kant’s refutation works so long as I am alive and am able to think about the existence of an external world, yet becomes difficult if I speculate on the consequences of my own nonexistence.”
Also these lines –
“No doubt I would cease to exist as a human consciousness, but would it also follow that the external world would also not exist.It is difficult to see how Kant could avoid this conclusion.” also show that answer is option (d).Incorrect
Soln. (d)
Fifth paragraph last line gives the clue to this question.
“Thus, Kant’s refutation works so long as I am alive and am able to think about the existence of an external world, yet becomes difficult if I speculate on the consequences of my own nonexistence.”
Also these lines –
“No doubt I would cease to exist as a human consciousness, but would it also follow that the external world would also not exist.It is difficult to see how Kant could avoid this conclusion.” also show that answer is option (d). 
Question 46 of 100
46. Question
Category: Reading ComprehensionQ.46. What is the authors stance regarding Kant’s views on the objectivity of external world?
Correct
Soln. (c)
Look at these lines –
“This relational objectivity does not necessary imply an ontological objectivity. Kant can defend his view of the external world against idealism, so long as he frames the charge of idealism at the relational qualities of objectivity.”
The author states that Kant can defend his theory of objectivity of external world but it does not imply ontological objectivity.
So he partially agrees with Kant but believes that Kants view are not complete.
The author doesn’t exactly criticize Kants view as he himself later says that the external world is ontologically objective.
(c) is a more correct answer compared to (b).Incorrect
Soln. (c)
Look at these lines –
“This relational objectivity does not necessary imply an ontological objectivity. Kant can defend his view of the external world against idealism, so long as he frames the charge of idealism at the relational qualities of objectivity.”
The author states that Kant can defend his theory of objectivity of external world but it does not imply ontological objectivity.
So he partially agrees with Kant but believes that Kants view are not complete.
The author doesn’t exactly criticize Kants view as he himself later says that the external world is ontologically objective.
(c) is a more correct answer compared to (b). 
Question 47 of 100
47. Question
Category: Reading ComprehensionQ.47. Why do you think Kant introduced the term called Noumena?
Correct
Soln. (b)
The question is why Kant introduced the term noumena. The question doesn’t ask you how Kant defends the existence of noumena.
Look at these lines –
“Kant argued that they must exist because phenomena are appearances, thus they must be appearances of something and that something must be noumena.”
This tells why option (a) is wrong.
These lines will tell you why Option (b) is only correct
“Kant was aware that the external world was limited by our understanding, and noumena are introduced partly as proof of this (i.e. noumena are the limits of human understanding).
It is the noumena that play the role of independent existences beyond the thinking subject.”Incorrect
Soln. (b)
The question is why Kant introduced the term noumena. The question doesn’t ask you how Kant defends the existence of noumena.
Look at these lines –
“Kant argued that they must exist because phenomena are appearances, thus they must be appearances of something and that something must be noumena.”
This tells why option (a) is wrong.
These lines will tell you why Option (b) is only correct
“Kant was aware that the external world was limited by our understanding, and noumena are introduced partly as proof of this (i.e. noumena are the limits of human understanding).
It is the noumena that play the role of independent existences beyond the thinking subject.” 
Question 48 of 100
48. Question
Category: Reading ComprehensionPassage 4
Directions for Q.48 to Q.52 – Read the following passage and answer the questions that follow.
With the 2005 publication of Steven Levitt’s Freakonomics, the world has come to see that economists can be spectacularly clever. In the search for “clean identification” — a situation in which it is easy to discern the causal forces in play —Levitt has turned to such offbeat contexts as Japanese sumowrestling and the seedy world of Chicago real estate. He has studied racial discrimination on a game show and reflected on whitecollar bagel filching. This has inspired a flurry of imitators, including papers on point shaving in college basketball, underused gym memberships and the parking tickets of UN diplomats. Within the tedious body of economics scholarship, these papers stand out as fantastically entertaining. Judging from the dizzying sales of Freakonomics and the thousands of lecture halls across the U.S. now bursting with econ majors, they’ve also been wildly successful at ginning up interest in the discipline. But what if all the cleverness has crowded out some of the truly deep questions we rely on economists to answer?
For more than a generation after the Second World War, the economists who dealt with real world data were mostly earnest, stubborn men. They tackled the era’s thorniest questions. Zvi Griliches of Harvard devoted decades to the problem of productivity growth, the chief determinant of rising living standards. His colleague Simon Kuznets spent half his career devising the measure of economic growth we still use today.
In the ‘80s, however, the datacrunchers had a crisis of confidence. In one famous episode, the eminent economist Gregg Lewis reviewed several studies on unions. Some papers reported that unions strongly increased wages; others reported exactly the opposite. The old approach had been sweeping in its ambition. But what good were ambitious goals if the best you could do was “on the one hand/on the other hand”style equivocation or plain gibberish? Many economists concluded that the path to knowledge lay in solid answers to modest questions. Henceforth, the emphasis would be on “clean identification.” “I’ve always been someone who’s thought it’s better to answer a small question well than to fail to answer a big question,” Levitt says. While still a student, he wondered whether money drives election results or if the better candidate raises more money. He ingeniously demonstrated the latter. Another early paper found that a slight increase in the chance of arrest dramatically deterred auto theft. Levitt discerned this by studying cities that had approved the use of Lojack,a transmitter that leads police to stolen cars. In 2001, Levitt published his most controversial finding: a paper highlighting the connection between the legalization of abortion in the ‘70s and the falling crime rates of the ‘90s. Levitt argued that unwanted children are most at risk of becoming criminals. Abortion, he concluded, lowered crime rates by reducing unwanted pregnancies. Some of these papers made important contributions. The Lojack paper helped demonstrate that theft is a rational phenomenon and can,therefore, be discouraged.
A few years later, Levitt debuted a new kind of paper: an investigation into offbeat phenomena from daily life. One pondered the strategies soccer players employ when taking penalty kicks. Another paper studied corruption in sumo wrestling tournaments as a window onto the power of incentives. Not long after, Levitt conducted an exhaustive inquiry into Weakest Link, a game show in which contestants voted to remove a player after each round of trivia questions. Tallying the voting data revealed that contestants were discriminating against Latinos and the elderly, but not blacks and women.
But while the game show provided a pure setting for observing discrimination, there was no reason to think we could extrapolate from Weakest Link contestants to hiring and promotion decisions, where discrimination often intersects with economics. Most such decisions don’t take place in a Hollywood studio before a national TV audience.
Levitt’s voice is high, except when it’s trailing off at the end of a sentence. He leans heavily on the word “OK.” He is lanky and concavechested and makes little eye contact. But Levitt has a droll magnetism, an anticharisma, which, combined with his eclectic interests, made a talk he gave at Harvard in 2002 a hit. “He talked about his kickass creative papers,” recalls one attendee. “Here are the lessons you can draw to improve your own research, how you can do clever, appealing papers yourself.” As he was wrapping up, Levitt reflected on the choices facing grad students: If you think you can do as well in traditional topics as someone like Marty Feldstein — a giant of the profession — you should pursue that, he said. Knowing laughter broke out. But, he continued, if you don’t feel like you’re up to that, you might want to think about alternative topics. The message resonated. One student watched classmates spend the next several weeks on high alert for some curiosity of daily life around which they could build a paper. Levitt has become famous for saying that “economics is a science with excellent tools for gaining answers but a serious shortage of interesting questions.” What is one to make of a discipline that heaps scorn on its own raison d’etre?
When I raise this with Levitt, he is almost apologetic: “There needs to be a core for work on the periphery to make any sense. I don’t think we would want to have a whole profession with dilettantes like me out doing what I do.” But he quickly adds: “The simple fact is that it’s hard to do good research. To the extent that you can do interesting research that teaches us something about the world, and entertains along the way, that’s not so bad.”
Q.48. According to the passage, the 1980’s saw the datacrunchers:
Correct
Soln. Option (b)
Consider the line, “In the ‘80s, however, the datacrunchers had a crisis of confidence.” This sentence opens the section that describes the predicament being faced by the data crunchers. The relevant paragraph talks about how the economists failed to answer questions well because of their uncertainty. This is reflected only in option (b) and hence it is the correct answer.Incorrect
Soln. Option (b)
Consider the line, “In the ‘80s, however, the datacrunchers had a crisis of confidence.” This sentence opens the section that describes the predicament being faced by the data crunchers. The relevant paragraph talks about how the economists failed to answer questions well because of their uncertainty. This is reflected only in option (b) and hence it is the correct answer. 
Question 49 of 100
49. Question
Category: Reading ComprehensionQ.49. It cannot be concluded that many old day economists who dealt with real world data ended up:
Correct
Soln. Option (d)
In the paragraph that talks about the economists in the ‘80s, consider the line, “Many economists concluded that the path to knowledge lay in solid answers to modest questions. This is pertaining to the ‘80s economists and hence tackling modest questions cannot be attributed to old day economists. All the other options are in the context of old day economists. This can be seen from the lines “For more than a generation after the Second World War, the economists who dealt with real world data were mostly earnest, stubborn men. They tackled the era’s thorniest questions. Zvi Griliches of Harvard devoted decades to the problem of productivity growth, the chief determinant of rising living standards. His colleague Simon Kuznets spent half his career devising the measure of economic growth we still use today.” Hence option (d) is the correct answer.Incorrect
Soln. Option (d)
In the paragraph that talks about the economists in the ‘80s, consider the line, “Many economists concluded that the path to knowledge lay in solid answers to modest questions. This is pertaining to the ‘80s economists and hence tackling modest questions cannot be attributed to old day economists. All the other options are in the context of old day economists. This can be seen from the lines “For more than a generation after the Second World War, the economists who dealt with real world data were mostly earnest, stubborn men. They tackled the era’s thorniest questions. Zvi Griliches of Harvard devoted decades to the problem of productivity growth, the chief determinant of rising living standards. His colleague Simon Kuznets spent half his career devising the measure of economic growth we still use today.” Hence option (d) is the correct answer. 
Question 50 of 100
50. Question
Category: Reading ComprehensionQ.50. Which one of the following is eminent on Levitt’s wish list for economists:
Correct
Soln. Option (d)
“I’ve always been someone who’s thought it’s better to answer a small question well than to fail to answer a big question,” Levitt says. This combined with ‘equivocation or plain gibberish’ mentioned earlier leads to option (d) as the correct answer.Incorrect
Soln. Option (d)
“I’ve always been someone who’s thought it’s better to answer a small question well than to fail to answer a big question,” Levitt says. This combined with ‘equivocation or plain gibberish’ mentioned earlier leads to option (d) as the correct answer. 
Question 51 of 100
51. Question
Category: Reading ComprehensionQ.51. According to the author, the voting data from the show ‘Weakest Link’ proved that:
Correct
Soln. Option (d)
Option (b) cannot be inferred as there is no data in the passage to support it. Option (b) talks about the economy of the show which is not mentioned anywhere in the passage. Option (c) brings in discrimination which is again not mentioned. Hence option (d) is the correct answer.Incorrect
Soln. Option (d)
Option (b) cannot be inferred as there is no data in the passage to support it. Option (b) talks about the economy of the show which is not mentioned anywhere in the passage. Option (c) brings in discrimination which is again not mentioned. Hence option (d) is the correct answer. 
Question 52 of 100
52. Question
Category: Reading ComprehensionQ.52. According to the passage, Levitt can be summed up as:
Correct
Soln. Option (d)
The entire passage deals with Levitt’s quintessential style of cracking problems and reaching answers using experiences at the micro level to deal with the ones at the conventional and
macro level. This makes option (d) correct. To call Levitt a dilettante(A person who claims an area of interest, such as the arts, without real commitment or knowledge) would not be correct.Incorrect
Soln. Option (d)
The entire passage deals with Levitt’s quintessential style of cracking problems and reaching answers using experiences at the micro level to deal with the ones at the conventional and
macro level. This makes option (d) correct. To call Levitt a dilettante(A person who claims an area of interest, such as the arts, without real commitment or knowledge) would not be correct. 
Question 53 of 100
53. Question
Category: Reading ComprehensionPassage 5
Directions for Q.53 to Q.55 – The passage is followed by questions based on its content. After reading the passage, choose the best answer to each question. Answer all questions about the passage on the basis of what is stated or implied in the passage.
Thomas Hardy’s impulses as a writer, all of which he indulged in his novels, were numerous and divergent, and they did not always work together in harmony. Hardy was to some degree interested in exploring his characters’ psychologies, though impelled less by curiosity than by sympathy. Occasionally he felt the impulse to comedy (in all its detached coldness) as well as the impulse to farce, but he was more often inclined to see tragedy and record it. He was also inclined to literary realism in the several senses of that phrase. He wanted to describe ordinary human beings; he wanted to speculate on (speculate on: v.考虑, 推测) their dilemmas rationally (and, unfortunately, even schematically); and he wanted to record precisely the material universe. Finally, he wanted to be more than a realist. He wanted to transcend what he considered to be the banality of solely recording things exactly and to express as well his awareness of the occult and the strange.
In his novels, these various impulses were sacrificed to each other inevitably and often. Inevitably, because Hardy did not care in the way that novelists such as Flaubert or James cared, and therefore took paths of least resistance. Thus, one impulse often surrendered to a fresher one and, unfortunately, instead of exacting a compromise, simply disappeared. A desire to throw over reality a light that never was might give way abruptly to the desire on the part of (on the part of: with regard to the one specified)what we might consider a novelistscientist to record exactly and concretely the structure and texture of a flower. In this instance, the new impulse was at least an energetic one, and thus its indulgence did not result in a relaxed style. But on other occasions, Hardy abandoned a perilous, risky, and highly energizing impulse in favor of what was for him the fatally relaxing impulse to classify and schematize abstractly. When a relaxing impulse was indulged, the style—that sure index of an author’s literary worth—was certain to become verbose. Hardy’s weakness derived from his apparent inability to control the comings and goings of these divergent impulses and from his unwillingness to cultivate and sustain the energetic and risky ones. He submitted to thefirst one and then another, and the spirit blew where it listed (愿意,想要); hence the unevenness of any one of his novels. His most controlled novel, Under the Greenwood Tree, prominently exhibits two different but reconcilable impulses—a desire to be a realisthistorian and a desire to be a psychologist of love—but the slight interlockings of the plot are not enough to bind the two completely together. Thus even this book splits into two distinct parts.
Q.53. The author of the passage considers a writer’s style to be
Correct
Soln. Option (A)
Let us look at these lines from the passage –
“When a relaxing impulse was indulged, the style—that sure index of an author’s literary worth”and (D) are pretty close choices.
The meaning of the word “Worth” is merit and not reputation.
So the answer is (a).Incorrect
Soln. Option (A)
Let us look at these lines from the passage –
“When a relaxing impulse was indulged, the style—that sure index of an author’s literary worth”and (D) are pretty close choices.
The meaning of the word “Worth” is merit and not reputation.
So the answer is (a). 
Question 54 of 100
54. Question
Category: Reading ComprehensionQ.54. Which of the following statements best describes the organization of lines “Thus, one impulse often …abstractly” of the passage?
Correct
Soln. Option (A)
Let us look at these lines from the passage –
“When a relaxing impulse was indulged, the style—that sure index of an author’s literary worth”and (D) are pretty close choices.
The meaning of the word “Worth” is merit and not reputation.
So the answer is (a).Incorrect
Soln. Option (A)
Let us look at these lines from the passage –
“When a relaxing impulse was indulged, the style—that sure index of an author’s literary worth”and (D) are pretty close choices.
The meaning of the word “Worth” is merit and not reputation.
So the answer is (a). 
Question 55 of 100
55. Question
Category: Reading ComprehensionQ.55. The author implies which of the following about “Under the Greenwood Tree” in relation to Hardy’s other novels?
Correct
Soln. (c)
It was a close choice between (C) and (D).
“His most controlled novel, Under the Greenwood Tree, prominently exhibits two different but reconcilable impulses—a desire to be a realisthistorian and a desire to be a psychologist of love—but the slight interlockings of the plot are not enough to bind the two completely together. Thus even this book splits into two distinct parts.”
He says that even this book splits into two parts. But nowhere has he said that all of hardy’s books are split into two parts. So (D) is wrong.Incorrect
Soln. (c)
It was a close choice between (C) and (D).
“His most controlled novel, Under the Greenwood Tree, prominently exhibits two different but reconcilable impulses—a desire to be a realisthistorian and a desire to be a psychologist of love—but the slight interlockings of the plot are not enough to bind the two completely together. Thus even this book splits into two distinct parts.”
He says that even this book splits into two parts. But nowhere has he said that all of hardy’s books are split into two parts. So (D) is wrong. 
Question 56 of 100
56. Question
Category: Reading ComprehensionPassage 6
Directions for Q.56 to Q.58 – The passage is followed by questions based on its content. After reading the passage, choose the best answer to each question. Answer all questions about the passage on the basis of what is stated or implied in the passage.
As the Moorish states in all parts of Spain fell into progressive political, military, and literary decadence, the atmosphere of the established Christian centers became increasingly more favorable to an intensive and varied literary development. The growth of cities had produced a comparatively urban and cultured population with sufficient leisure and security to find time for literary entertainment. The growth of commerce had brought Spaniards into contact with other societies that had developed original and stimulating literary traditions. The growth of a recognized and responsible central government, following the definitive unification of Castile and León under Ferdinand III early in the thirteenth century, had provided a court or central cultural focus toward which men of literary ability could gravitate. The growing selfawareness of the writer as a unique creative personality, from the anonymity of the cantares de gestato the tentative identification we see in the poetry of Berceo, to intense and affirmative individualism of the later mesterdeclerecíain Juan Ruiz and López de Ayala, demands an ever broader field in which to realize and fulfill itself. In obedience to this sort of aesthetic need and nurtured on the expanding possibilities of a settled and prospering society, the fifteenth century represents a period of great fecundity in the development and widening of literary genres.
The medieval cantar de gesta, which had so magnificently served the needs of a society of embattled warriors, undergoes a major change, possibly through the influence of the mester de clerecía. In the new society there was neither time, place, nor public for the recitation of the long and usually complex epic poems, but the great deeds, the great heroes still held their magic for the general public. These survive in a new poetic form, the romances. The anonymous romances are short poems of regular meter and assonance which capture an intense and dramatic moment—of sorrow, of defeat, of parting, of return—in simple and direct language. They are generally fragmentary, combining lyricism and narration taken from the dramatic high points of the epics. Some critics have thought that the oldest romances represent a survival of the raw material from which the long cantaresgrew, but the more generally accepted opinion is that they represent the opposite process; as the old cantaresfell into oblivion, the best moments and the most stirring passages were conserved and polished and given new life.
Supporting this view is the fact that the earliest romances go back only to the middle of the fourteenth century, a time in which the cantareswere in a period of final decadence and the oldest epic poems already forgotten. They share the realism and directness of the cantares, and also the greater polish and lyricism of the mester de clerecía. Some thousands of them have been collected and not all relate to the material of the Spanish epics.
Q.56.The passage implies that
Correct
Soln.(b).
The implication is that the cantaresweremore often recited in public than read in private. Choice A is incorrect. The romancescombine lyricism with narration taken from the dramatic high points ofthe epics; nothing suggests that they are concerned with peace rather than war.
Notice that defeat is mentioned as one of the moments captured by romances.
Eliminate choice A. The passage does not refer to Moorish influence on any of the genres, so choice C can be eliminated. Choice Dis a reversal of what the passage suggests.Eliminate choice D.Incorrect
Soln.(b).
The implication is that the cantaresweremore often recited in public than read in private. Choice A is incorrect. The romancescombine lyricism with narration taken from the dramatic high points ofthe epics; nothing suggests that they are concerned with peace rather than war.
Notice that defeat is mentioned as one of the moments captured by romances.
Eliminate choice A. The passage does not refer to Moorish influence on any of the genres, so choice C can be eliminated. Choice Dis a reversal of what the passage suggests.Eliminate choice D. 
Question 57 of 100
57. Question
Category: Reading ComprehensionQ.57.From the passage the reader can infer that
Correct
Soln. (c).
The author cites Spaniards’ contact with other societies as apositive influence on Spain’s literary development (lines 6–8). The statements inboth choices A and B are far too sweeping, based on information in the passage.Choice D is not mentioned or implied, and nothing suggests that the mester declerecíawere more popular than the epics.Incorrect
Soln. (c).
The author cites Spaniards’ contact with other societies as apositive influence on Spain’s literary development (lines 6–8). The statements inboth choices A and B are far too sweeping, based on information in the passage.Choice D is not mentioned or implied, and nothing suggests that the mester declerecíawere more popular than the epics. 
Question 58 of 100
58. Question
Category: Reading ComprehensionQ.58. According to the passage, the theory that the romances come from the same raw material as the cantaresis questionable because
Correct
Soln. (a).
According to the author, the cantareswere in a period of“final decadence” at the time the romances were born, so it is unlikely that theycame from the same raw material. Choice B is incorrect; the subject matter ofromanceswas not the lives of everyday people. In lines 23–24 the cantaresaredescribed as “usually complex,” whereas in line 28 the romances are characterizedas written in “simple and direct” language, making choice C also a badchoice. Since the subject matter of romances often derives from the epics, choiceD is also incorrect.Incorrect
Soln. (a).
According to the author, the cantareswere in a period of“final decadence” at the time the romances were born, so it is unlikely that theycame from the same raw material. Choice B is incorrect; the subject matter ofromanceswas not the lives of everyday people. In lines 23–24 the cantaresaredescribed as “usually complex,” whereas in line 28 the romances are characterizedas written in “simple and direct” language, making choice C also a badchoice. Since the subject matter of romances often derives from the epics, choiceD is also incorrect. 
Question 59 of 100
59. Question
Category: Verbal AbilityVerbal Ability:
Directions for questions Q.5960: The question consists of four sentences on a topic. Type the answer choices corresponding to the sentences that are correct in terms of grammar in the box below the sentence. For example, if the correct sentences are B and D, type in BD in the box.
Q.59.
 Large reductions in the ozone layer, which sits about 1530 km above the Earth, take place each winter over the Polar regions, especially the Antarctic, as low temperatures allow the formation of stratospheric clouds that assist chemical reactions breaking down ozone.
 Industrial chemicals containing chlorine and bromine have been blamed for thinning the layer because they attack the ozone molecules, making them to break apart.
 Many an offending chemicals have now been banned.
4. It will still take several decades before these substances have disappeared from the atmosphere.
Correct
Soln. Option (b)
Statements 2 and 3 are incorrect. Statement 2 is incorrect because ‘to break apart’ is an incorrect idiom. It should be “making them break apart” the verb ‘make’ is not followed by an infinitive (to+verb). E.g. It makes me cry and not It makes me to cry.
Statement C is incorrect because of ‘many an offending chemicals’. The correct versions will be ‘many offending chemicals (have)’ or many an offending chemical (has)’. Statements 1 and 4 are both correct.Incorrect
Soln. Option (b)
Statements 2 and 3 are incorrect. Statement 2 is incorrect because ‘to break apart’ is an incorrect idiom. It should be “making them break apart” the verb ‘make’ is not followed by an infinitive (to+verb). E.g. It makes me cry and not It makes me to cry.
Statement C is incorrect because of ‘many an offending chemicals’. The correct versions will be ‘many offending chemicals (have)’ or many an offending chemical (has)’. Statements 1 and 4 are both correct. 
Question 60 of 100
60. Question
Category: Verbal AbilityQ.60.
 When virtuoso teams begin their work, individuals are in and group consensus is out.
 As project progresses, however, the individual stars harness themselves to the product of the group.
 Sooner or later, the members break through their own egocentrism and become a plurality with singleminded focus on the goal.
 In short, they morph into a powerful team with a shared identity.
Correct
Soln. Option (b)
Statements 2 and 3 are incorrect.
Statement B is incorrect because ‘As project progresses’ should be corrected to “As the project progresses…” The (definite or indefinite) article is required as a determiner. Statement C is incorrect in the phrase ‘a plurality with singleminded focus’ – should be corrected to “a plurality with a singleminded focus…” The noun ‘focus’ needs a determiner (definite/indefinite article). Hence, the correct statements are 1 and 4.Incorrect
Soln. Option (b)
Statements 2 and 3 are incorrect.
Statement B is incorrect because ‘As project progresses’ should be corrected to “As the project progresses…” The (definite or indefinite) article is required as a determiner. Statement C is incorrect in the phrase ‘a plurality with singleminded focus’ – should be corrected to “a plurality with a singleminded focus…” The noun ‘focus’ needs a determiner (definite/indefinite article). Hence, the correct statements are 1 and 4. 
Question 61 of 100
61. Question
Category: Verbal AbilityDirections for questions 6164: Each of the following questions has a paragraph from which the last sentence has been deleted. Type the answer choice that completes the paragraph in the most appropriate way.
Q.61. Politics is about power and its legitimacy. It is not about the extremely regressive and reactionary idea of civil society that unthinking commentators seem to be offering, day in and day out. Constant harping on civil society leads to sentimentality, nostalgia and illiberalism of the worst kind, along with malignant notions of nationalism and communitarianism.___________________
Correct
Soln. Option (b)
The paragraph starts with an ideology of what politics is actually and what it is made to be. The concluding sentence, will thus, talk about who has pioneered this ideology.
B is the best option.Incorrect
Soln. Option (b)
The paragraph starts with an ideology of what politics is actually and what it is made to be. The concluding sentence, will thus, talk about who has pioneered this ideology.
B is the best option. 
Question 62 of 100
62. Question
Category: Verbal AbilityQ.62. In the 1920s, Riga was where Kremlin watchers like Loy Henderson and George F. Kennan cut their teeth. Other members of this group, which drove U.S. foreign policy towards the Soviet Union in the prewar period, were James Forrestal, the Dulles brothers, and William Bullitt._______________________
Correct
Soln. Option (a)
This question is taken from an editorial. Option (b),(c),(d) actually follow option (a) in the editorial, which in turn is the last sentence of the paragraph. Option (a) is the correct answer
Incorrect
Soln. Option (a)
This question is taken from an editorial. Option (b),(c),(d) actually follow option (a) in the editorial, which in turn is the last sentence of the paragraph. Option (a) is the correct answer

Question 63 of 100
63. Question
Category: Verbal AbilityQ.63. 2005 is also the year we start implementing our new European Neighbourhood Policy (ENP). Having finally overcome 60 years of division in Europe, we are determined not to create a new set of dividing lines in Europe, and want to capitalise on our new members’ relations with their neighbours to project the EU’s stability, prosperity and security beyond our shores.___________________________
Correct
Soln. Option (c)
The paragraph talks about why the ENP policy will be good to implement and what it will put an end to. Option (c) is the best concluding line for this paragraph as it provides a gist of the advantages of the ENP policy.Incorrect
Soln. Option (c)
The paragraph talks about why the ENP policy will be good to implement and what it will put an end to. Option (c) is the best concluding line for this paragraph as it provides a gist of the advantages of the ENP policy. 
Question 64 of 100
64. Question
Category: Verbal AbilityQ.64. The official reactions to the London blackout were very revealing. The elected London Mayor, Ken Livingstone, had no hesitation in appearing on radio and television. The private electricity company, National Grid, put up a technical functionary who was obviously ill at ease and could only keep repeating the technical explanation for the shutdown.________________________________
Correct
Soln. Option (d)
The passage talks about the reasons for London’s blackout and how the private electricity company could not provide a satisfactory explanation. Option (d) is in logical continuance with this idea as it talks about how the press coverage won’t be much even though the mayor had no hesitation in appearing on radio and television. Option (a) is too vague and is eliminated. Option (b) predicts the future when this is not discussed in the passage. It is eliminated. Option (c) brings in pipedgas which goes outside the scope of the passage. So the correct answer is option (d).Incorrect
Soln. Option (d)
The passage talks about the reasons for London’s blackout and how the private electricity company could not provide a satisfactory explanation. Option (d) is in logical continuance with this idea as it talks about how the press coverage won’t be much even though the mayor had no hesitation in appearing on radio and television. Option (a) is too vague and is eliminated. Option (b) predicts the future when this is not discussed in the passage. It is eliminated. Option (c) brings in pipedgas which goes outside the scope of the passage. So the correct answer is option (d). 
Question 65 of 100
65. Question
Category: Verbal AbilityDirections for questions 6566: Each question is based on a word which is used in 4 sentences. Type the answer choice corresponding to the sentencewhere the usage of the word is inappropriate. For example, if the incorrect usage is in sentence B, type in B in the box.
Q.65. HANG
Correct
Soln. Option (d)
“Hangon” means “to hold fast to”. Its usage in the fourth sentence is wrong.
Incorrect
Soln. Option (d)
“Hangon” means “to hold fast to”. Its usage in the fourth sentence is wrong.

Question 66 of 100
66. Question
Category: Verbal AbilityQ.66. HARD
Correct
Soln. Option (c)
While one can work hard, one cannot write hard.
Incorrect
Soln. Option (c)
While one can work hard, one cannot write hard.

Question 67 of 100
67. Question
Category: Verbal AbilityDirections for questions 67 to 68:Four alternative summaries are given below each text. Type the answer choice corresponding to the sentence that best captures the essence of the text in the box below the sentences. For example, if the correct sentence is B, type in B in the box.
Q.67. Greece has both natural and cultural assets. But it has lacked in infrastructure — be it inadequate, or unsuitable public transport from the airport, or poor service at a restaurant, or in a shop. Representatives from across the sector of the Greek tourism industry — hoteliers, restaurant owners, travel agents, tour bus operators, tour guides, ferry companies, and so on — have long touted the problems they have faced. From its first day in government, the New Democracy indicated its intention to address these problems. And in the first few months it has been in power, it has already gone beyond simply stating its intentions and has actually begun to do something.
Correct
Soln. Option (a)
(a) is obviously the correct answer. It is an exact restatement of what is stated in the paragraph. (b) is an isolated statement, (c) is only partially complete, it may not be pertinent to Greece, and (d) is a fact not mentioned in the paragraph.
Incorrect
Soln. Option (a)
(a) is obviously the correct answer. It is an exact restatement of what is stated in the paragraph. (b) is an isolated statement, (c) is only partially complete, it may not be pertinent to Greece, and (d) is a fact not mentioned in the paragraph.

Question 68 of 100
68. Question
Category: Verbal AbilityQ.68. If one wishes to form a true estimate of the full grandeur of religion, one must keep in mind what it undertakes to do for men. It gives them information about the source and origin of the universe, it assures them of protection and final happiness amid the changing vicissitudes of life, and it guides their thoughts and actions by means of precepts which are backed by the whole force of its authority. It fulfils, therefore, three functions. In the first place, it satisfies man’s desire for knowledge; it is here doing the same thing that science attempts to accomplish by its own methods, and here, therefore, enters into rivalry with it. It is to the second function that it performs that religion no doubt owes the greater part of its influence. In so far as religion brushes away man’s fear of the dangers and vicissitudes of life, in so far as it assures them of a happy ending, and comforts them in their misfortunes, science cannot compete with it.
Correct
Soln. Option (b)
(b) is correct, it carries the crux of the paragraph. Refer to the part religion no doubt owes the greater part of its influence…. science cannot compete with it. (d) is doubtful, security is an ambiguous term. (c) contradicts information given in the paragraph. (a) is limited as the relative factor is not stated in the paragraph.Incorrect
Soln. Option (b)
(b) is correct, it carries the crux of the paragraph. Refer to the part religion no doubt owes the greater part of its influence…. science cannot compete with it. (d) is doubtful, security is an ambiguous term. (c) contradicts information given in the paragraph. (a) is limited as the relative factor is not stated in the paragraph. 
Question 69 of 100
69. Question
Category: Logical ReasoningDirections for questions 69 to 72: These questions are based on the following information.
Five friends – A, B, C, D and E met at a party. They live in different cities among – Delhi, Mumbai,
Bangalore, Chennai and Hyderabad and work in different companies among – Infotec, Quetec, Rototec,
Simotec and Tetratec, not necessarily in the same order. We know the following information about
them.
(a) A lives in Delhi but does not work in Quetec.
(b) C works in Tetratec.
(c) The person, who lives in Bangalore, works in Simotec
(d) Neither D nor B lives in Chennai.
(e) B works in Infotec and E lives in Hyderabad.
Q69. Who lives in Mumbai?Correct
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – QuetecIncorrect
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – Quetec 
Question 70 of 100
70. Question
Category: Logical ReasoningQ70. Which company does D work in?
Correct
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – QuetecIncorrect
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – Quetec 
Question 71 of 100
71. Question
Category: Logical ReasoningQ71. In which city does the person who works in Tetratec live?
Correct
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – QuetecIncorrect
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. => C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – Quetec 
Question 72 of 100
72. Question
Category: Logical ReasoningQ72. In which city does the person who works in Infotec live?
Correct
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. =>C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – QuetecIncorrect
Solution:
From (a), (b) and (c), as A lives in Delhi, he does not work in Simotec.
Also, he does not work in Quetec and Tetratec.
From (e), B works in Infotec =>A works in Rototec.
From (d) and (e), none of D, B and E lives in Chennai. =>C lives in Chennai.
From (c) and (d), as B works in Infotec, he does not live in Bangalore. =>D lives in Bangalore and works in Simotec.
E works in Quetec and B lives in Mumbai.
The distribution table is as follows.
A – Delhi – Rototec
C – Chennai – Tetratec
D – Bangalore – Simotec
B – Mumbai – Infotec
E – Hyderabad – Quetec 
Question 73 of 100
73. Question
Category: Logical ReasoningDirections for questions 7376: Answer the questions on the basis of the information given
below.
The following table gives the standings at a certain stage of a sixteam football tournament.
Each team plays with the other team only once. A game of football involves only two teams.
The team that scores more number of goals is the winner of that particular game. A game is
said to be a draw if the goals scored by both the teams is the same. The following nomenclature
holds true for the table, ‘P’ – Games played, ‘W’ – Games won, ‘L’ Games lost, ‘D’ – Games
drawn, ‘GF’ – Goals For, ‘GA’ Goals Against, ‘GD’ – Goal Difference, ‘Points’ – Total number of
points. Three points are awarded for a win, one for a draw and no points are awarded in case of
a loss. There is some data missing in the table.S.NO. Teams P W L D GF GA GD Points 1 Aston Villa 4 1 1 2 4 4 0 5 2 Sunderland 4 0 1 3 4 5 1 3 3 Fulham 4 0 1 3 3 4 1 3 4 Manchester United 4 2 0 2 6 4 2 8 5 Birmingham city 4 1 0 3 5 3 2 6 6 Chelsea 4 1 2 1 6 4 Additional information given:
(i) The total number of goals scored in each of the drawn games is 2.
(ii) Aston villa and Manchester United drew their games with Chelsea and Birmingham City
respectively.
(iii) Chelsea beats Sunderland.Q73. Find the number of goals scored in the game between Chelsea and Sunderland.
Correct
Solution:
Sunderland scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.
Hence it must have lost a game 12 because the number of goals scored against Sunderland is 5 and goals scored by Sunderland are 4.Therefore Sunderland lost its game to Chelsea 12. Hence number of goals scored in this game is 3.Incorrect
Solution:
Sunderland scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.
Hence it must have lost a game 12 because the number of goals scored against Sunderland is 5 and goals scored by Sunderland are 4.Therefore Sunderland lost its game to Chelsea 12. Hence number of goals scored in this game is 3. 
Question 74 of 100
74. Question
Category: Logical ReasoningQ74. Fulham lost its game with a Scoreline of
Correct
Solution:
Fulham scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.
Hence it must have lost a game 01 because the number of goals scored against Fulham is 4 and goals scored by Fulham are 3.Incorrect
Solution:
Fulham scored 3 goals 1 each of the drawn games and 3 goals were scored against them 1 each for 3 drawn games.
Hence it must have lost a game 01 because the number of goals scored against Fulham is 4 and goals scored by Fulham are 3. 
Question 75 of 100
75. Question
Category: Logical ReasoningQ75. How many goals has Chelsea scored in its 4 games?
Correct
Solution:
The goal difference of all teams must add up to 0.Hence GD of Chelsea = –2
If 6 goals have been scored against it, it must have scored 4 goals.Incorrect
Solution:
The goal difference of all teams must add up to 0.Hence GD of Chelsea = –2
If 6 goals have been scored against it, it must have scored 4 goals. 
Question 76 of 100
76. Question
Category: Logical ReasoningQ76. How many games have been played till now?
Correct
Solution:
There are 24 entries against matches played. But in a match there are 2 teams participating hence there is an entry against each team and hence counted twice. This means in all 24/2 =12 matches played.Incorrect
Solution:
There are 24 entries against matches played. But in a match there are 2 teams participating hence there is an entry against each team and hence counted twice. This means in all 24/2 =12 matches played. 
Question 77 of 100
77. Question
Category: Logical ReasoningDirections for Questions 7781: Answer the questions based on the information given below.
Schedule for the midterm examination for students in class IX in St Patrick’s School is prepared. There
are seven subjects: English, Physics, Chemistry, Mathematics, Biology, Computer Science and Economics.
The midterm examination is to be culminated in fortnight starting on Monday of first week and ending
on Saturday of the next week, there being no exam on Sunday. It is also known that:
I. There is a gap of 3 days between the schedules of Mathematics and English.
II. There is a gap of 1 week between the schedules of Physics and Mathematics.
III. There is exam on each day of the week except Sunday.
IV. There is no gap between the schedules of Biology and that of the subject that just precedes it.
V. The schedule Computer science follow that of Chemistry.Q77. Two of the exams fall on
Correct
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp Incorrect
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp 
Question 78 of 100
78. Question
Category: Logical ReasoningQ78. How many days are there between the schedules of English and Economics?
Correct
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp Incorrect
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp 
Question 79 of 100
79. Question
Category: Logical ReasoningQ79. How many days are there between the schedules of Economics and Biology?
Correct
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp Incorrect
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp 
Question 80 of 100
80. Question
Category: Logical ReasoningQ80. The schedule of which of the following subjects can be uniquely determined?
Correct
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp Incorrect
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp 
Question 81 of 100
81. Question
Category: Logical ReasoningQ81. In how many different ways, the schedules of all exams are possible?
Correct
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp Incorrect
Solution:
There can be two cases for the scheduled day of exams, since on every unique day of the week, there is atleast one exam:
Case I: Mon Tue Thur Sat Mon Wed Fri
This is not possible as exams end on Friday.
Case II Mon Wed Fri Sat Tue Thurs Sat Phy Chem Comp Bio Math Eco Eng Or Chem Comp Phy/Math Bio Eng Eco Math/Phy Or Eng Eco Math Bio Chem Comp Phy or Phy/Math Eco Eng Bio Math/Phy Chem Comp 
Question 82 of 100
82. Question
Category: Logical ReasoningDirections for questions 8285: Answer the questions based on the information given below.
In the mini – World Cup played at Bulawayo, five cricket teams viz. Australia, South Africa, India, New
Zealand and Pakistan participated in the tournament. Each team has to play exactly one match with
each of the other teams. If a team wins a match, it is awarded 2 points and gets no points for losing a
match. In case a match is a tie, then each of the two teams playing the match would be awarded a point.
None of the matches scheduled were abandoned.
After the tournament was over, it was known that the total sum of the points scored by some pairs of two teams is a follows:
i) Australia + India = 12
ii) India + South Africa = 11
iii) New Zealand + India = 10
iv) India + Pakistan = 8
Also, it is known that there were two ties in the tournament.
Q82. If it is known that South Africa won a match against Australia, then New Zealand tied their match
with which of the following teams?Correct
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have
the following possibilities of ties:
Case I: I ties with A, NZ ties with P
Team Win Lose Tie A (SA/NZ), P (SA or NZ) I SA (A or NZ), P A or NZ), I – I SA, NZ, P – A NZ (A or SA) (A or SA), I P P – A, SA, I NZ Case II: I ties with NZ, A ties with P.
Team Win Lose Tie A SA, NZ I P SA NZ, P A, I – I NZ, P – NZ NZ P A, SA I P – I, SA, NZ A Case III: I ties with P, A ties with NZ
Team Win Lose Tie A SA, P I NZ SA NZ, P A, I – I A, SA, NZ – P NZ P SA, I A P – A, SA, NZ I South Africa wins against Australia only in Case I, in which NZ ties with P.
Incorrect
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have
the following possibilities of ties:
Case I: I ties with A, NZ ties with P
Team Win Lose Tie A (SA/NZ), P (SA or NZ) I SA (A or NZ), P A or NZ), I – I SA, NZ, P – A NZ (A or SA) (A or SA), I P P – A, SA, I NZ Case II: I ties with NZ, A ties with P.
Team Win Lose Tie A SA, NZ I P SA NZ, P A, I – I NZ, P – NZ NZ P A, SA I P – I, SA, NZ A Case III: I ties with P, A ties with NZ
Team Win Lose Tie A SA, P I NZ SA NZ, P A, I – I A, SA, NZ – P NZ P SA, I A P – A, SA, NZ I South Africa wins against Australia only in Case I, in which NZ ties with P.

Question 83 of 100
83. Question
Category: Logical ReasoningQ83. How many total arrangements of wins and ties are possible?
Correct
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have
the following possibilities of ties:
Case I: I ties with A, NZ ties with P
Team Win Lose Tie A (SA/NZ), P (SA or NZ) I SA (A or NZ), P A or NZ), I – I SA, NZ, P – A NZ (A or SA) (A or SA), I P P – A, SA, I NZ Case II: I ties with NZ, A ties with P.
Team Win Lose Tie A SA, NZ I P SA NZ, P A, I – I NZ, P – NZ NZ P A, SA I P – I, SA, NZ A Case III: I ties with P, A ties with NZ
Team Win Lose Tie A SA, P I NZ SA NZ, P A, I – I A, SA, NZ – P NZ P SA, I A P – A, SA, NZ I Total number of arrangements
Case I = 2
Case II = 1
Case III = 1
——–
4
——–Incorrect
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)As there are two ties they must be between A, NZ, I and P, but not SA. Now we can have
the following possibilities of ties:
Case I: I ties with A, NZ ties with P
Team Win Lose Tie A (SA/NZ), P (SA or NZ) I SA (A or NZ), P A or NZ), I – I SA, NZ, P – A NZ (A or SA) (A or SA), I P P – A, SA, I NZ Case II: I ties with NZ, A ties with P.
Team Win Lose Tie A SA, NZ I P SA NZ, P A, I – I NZ, P – NZ NZ P A, SA I P – I, SA, NZ A Case III: I ties with P, A ties with NZ
Team Win Lose Tie A SA, P I NZ SA NZ, P A, I – I A, SA, NZ – P NZ P SA, I A P – A, SA, NZ I Total number of arrangements
Case I = 2
Case II = 1
Case III = 1
——–
4
——– 
Question 84 of 100
84. Question
Category: Logical ReasoningQ84. Which of the following teams stand 3 rd position?
Correct
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)Third highest points are scored by South Africa
Incorrect
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)Third highest points are scored by South Africa

Question 85 of 100
85. Question
Category: Logical ReasoningQ85. Which of the following statements must be true?
Correct
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)Only South Africa must have won against Pakistan, as others have a chance of tying a match with Pakistan.
Incorrect
Solution:
Let us take the first letter of the name of each team to represent its name. Now, it is given
That
 A + I = 12
 I + SA = 11
 NZ + I = 10
 I + P = 8
Adding the above four equations, we get:
A + SA + 4I + NZ + P = 41 …….. (1)
The total number of games played is = 4 + 3 + 2 + 1 = 10
Each game is worth two points hence total points = 10 x 2 = 20or A + SA + I + NZ + P = 20 …….(2)
Comparing with equation (1) and (2) we get:
3I = 21 or I = 7 (3 wins, 1 tie)
A = 5(2 win, 1 tie), SA = 4(2 wins), NZ = 3(1 win, 1 tie), P=1(1 tie)Only South Africa must have won against Pakistan, as others have a chance of tying a match with Pakistan.

Question 86 of 100
86. Question
Category: Data InterpretationDirections for questions 8690:
In a University examination, six students, Sachin, Ashish, Tanwi, Ankit, Ramesh and Suresh had
written the following three papers, Economics, Finance and Accounts. The examination
comprised of two parts, internals and externals. The table below shows the performance of
each of these six students in this examination.
Part A: Indicates the total marks scored by the student in that paper as a percentage of the
total marks of all the six students put together in that subject.
Part B: Indicates the marks scored by that student in internals as a percentage of total marks
scored by that student in that subject.
From the table below it can be inferred that Sachin had obtained 30% of marks in Economics
out of the total marks obtained by all the six students in Economics put together. Whereas out
of the marks scored by him in Economics, the marks scored by him in Internals accounted for
20% of marks.Economics Finance Accounts
Part A Part B Part A Part B Part A Part B
Sachin 30 20 25 10 25 10
Ashish 10 35 10 0 20 5
Tanwi 15 25 10 10 10 0
Ankit 10 30 5 10 10 10
Ramesh 20 40 20 10 30 25
Suresh 15 15 30 5 5 10Q86. If the ratio of marks obtained by Ankit in the internals of all three subjects (Economics,
Finance and Accounts) in that order is 9:3: 4, then what was the ratio of marks scored by Sachin
in the externals of those three subjects in the same order?Correct
Sol: Option (c)
Let the total marks scored by the six students in Economics, Finance and Accounts be x, y and z respectively.
∴ The ratio of marks scored by Ankit in the Internals of these papers would be:
(30% of 10% of x) : (10% of 5% of y) : (10% of 10% of z) which would be the same as (0.03x) : (0.005y) : (0.01z) = (3x) : (0.5y) : (z)
But, (3x) : (0.5y) : (z) is equal to 9 : 3 : 4.
∴3x = 9, 0.5y = 3 and z = 4
∴ The ratio x: y: z would be equal to 3:6: 4.
The marks scored by Sachin are 30%, 25% and 25%, the ratio of marks would be 90:150: 100, i.e. 9:15: 10.
Now, the marks scored by Sachin in Internals are 20%, 10% and 10%.
∴ Marks scored by him in Externals will be 80%, 90% and 90%.
∴ The required ratio would be (80% of 9) : (90% of 15) : (90% of 10), i.e. (7.2) : (13.5) : (9)
This ratio would be equal to 72 : 135 : 90 or 24 : 45 : 30Incorrect
Sol: Option (c)
Let the total marks scored by the six students in Economics, Finance and Accounts be x, y and z respectively.
∴ The ratio of marks scored by Ankit in the Internals of these papers would be:
(30% of 10% of x) : (10% of 5% of y) : (10% of 10% of z) which would be the same as (0.03x) : (0.005y) : (0.01z) = (3x) : (0.5y) : (z)
But, (3x) : (0.5y) : (z) is equal to 9 : 3 : 4.
∴3x = 9, 0.5y = 3 and z = 4
∴ The ratio x: y: z would be equal to 3:6: 4.
The marks scored by Sachin are 30%, 25% and 25%, the ratio of marks would be 90:150: 100, i.e. 9:15: 10.
Now, the marks scored by Sachin in Internals are 20%, 10% and 10%.
∴ Marks scored by him in Externals will be 80%, 90% and 90%.
∴ The required ratio would be (80% of 9) : (90% of 15) : (90% of 10), i.e. (7.2) : (13.5) : (9)
This ratio would be equal to 72 : 135 : 90 or 24 : 45 : 30 
Question 87 of 100
87. Question
Category: Data InterpretationQ87. If, in the case of Ramesh, the marks scored by him in Externals in Finance is less than that scored by him in Economics and Accounts, then what is the ratio of total marks scored by all students in Finance put together to the total marks scored by all six students in all the subjects put together?
Correct
Sol: Option (E)
As we have only comparative ratios and not the exact ratios, we cannot find the required value.Incorrect
Sol: Option (E)
As we have only comparative ratios and not the exact ratios, we cannot find the required value. 
Question 88 of 100
88. Question
Category: Data InterpretationQ88. If the total marks scored by Ramesh in Economics and Accounts are the same, then for how many students from these six is the total marks scored in Economics more than twice the total marks scored by them in Accounts?
Correct
Soln. Option (b)
Student Economics (300) Accounts(200) Percentage Marks Percentage Marks Sachin 30 90 25 50 Ashish 10 30 20 40 Tanwi 15 45 10 20 Ankit 10 30 10 20 Ramesh 20 60 30 60 Suresh 15 45 5 10 In case of Ramesh, the marks scored by him in Economics, Finance and Accounts are 20%, 20% and 30% respectively out of the total marks scored by all the students put together.
∴ 20% of the total marks of all the students in Economics = 30% of the total marks of all the students in Accounts.
∴ The ratio of the total marks scored by all six students put together in Economics to that of Accounts will be 3: 2.
For simplicity, assume that the total number of marks obtained by all of them in Economics be 300 and in Accounts be 200.
Now the results can be tabulated by taking the marks in the required ratio as shown above.
∴there are only 2 students satisfying the criteria.Incorrect
Soln. Option (b)
Student Economics (300) Accounts(200) Percentage Marks Percentage Marks Sachin 30 90 25 50 Ashish 10 30 20 40 Tanwi 15 45 10 20 Ankit 10 30 10 20 Ramesh 20 60 30 60 Suresh 15 45 5 10 In case of Ramesh, the marks scored by him in Economics, Finance and Accounts are 20%, 20% and 30% respectively out of the total marks scored by all the students put together.
∴ 20% of the total marks of all the students in Economics = 30% of the total marks of all the students in Accounts.
∴ The ratio of the total marks scored by all six students put together in Economics to that of Accounts will be 3: 2.
For simplicity, assume that the total number of marks obtained by all of them in Economics be 300 and in Accounts be 200.
Now the results can be tabulated by taking the marks in the required ratio as shown above.
∴there are only 2 students satisfying the criteria. 
Question 89 of 100
89. Question
Category: Data InterpretationQ89. If Suresh had scored 20 marks in Accounts and 45 marks in Finance, then the marks scored by all six students in internals of these 2 subjects would be (All marks, at all stages of evaluation, have to be integers. So, round off any decimal to the next higher number)
Correct
Solution : Option (A)
Finance(150) Accounts (400) Student Total Internal Total Internal Percentage Marks Percentage Marks Percentage Marks Percentage Marks Sachin 25 37.5 10 4 25 100 10 10 Ashish 10 15 0 0 20 80 5 4 Tanwi 10 15 10 2 10 40 0 0 Ankit 5 7.5 10 1 10 40 10 4 Ramesh 20 30 10 3 30 120 25 30 Suresh 30 45 5 3 5 20 10 2 Suresh scoring 20 marks in Accounts implies that the total marks scored by all six students put together would be 400 as his marks constituted 5% of the total marks.
Similarly, the total marks scored by all six students put together in Finance would be 150 as his
marks constituted 30% of the total marks.
The results can be tabulated as shown above.
∴The total marks scored by all six students in the internals of Finance are 13 and that inAccounts is 50.
∴The required total is 63.Incorrect
Solution : Option (A)
Finance(150) Accounts (400) Student Total Internal Total Internal Percentage Marks Percentage Marks Percentage Marks Percentage Marks Sachin 25 37.5 10 4 25 100 10 10 Ashish 10 15 0 0 20 80 5 4 Tanwi 10 15 10 2 10 40 0 0 Ankit 5 7.5 10 1 10 40 10 4 Ramesh 20 30 10 3 30 120 25 30 Suresh 30 45 5 3 5 20 10 2 Suresh scoring 20 marks in Accounts implies that the total marks scored by all six students put together would be 400 as his marks constituted 5% of the total marks.
Similarly, the total marks scored by all six students put together in Finance would be 150 as his
marks constituted 30% of the total marks.
The results can be tabulated as shown above.
∴The total marks scored by all six students in the internals of Finance are 13 and that inAccounts is 50.
∴The required total is 63. 
Question 90 of 100
90. Question
Category: Data InterpretationQ90. If the marks scored by Sachin in the internals of Economics are same as that scored by Ashish in the internals of Accounts, then what is the ratio of the total marks scored by all six students in Economics put together to that scored in Accounts put together?
Correct
Sol. Option (A)
Let the total marks scored by all six students put together in Economics be ‘x’ and that in Accounts be ‘y’.
Then the total marks scored by Sachin in Economics = 30% of x
∴ Marks scored by Sachin in the internals of Economics = 20% of 30% of x = 0.06x
Similarly, the total marks scored by Ashish in Accounts = 20% of y
∴ Marks scored by Ashish in the internals of Accounts = 5% of 20% of y = 0.01y
From the condition given in the question, both these marks are equal.
∴ 0.06x = 0.01y
∴ x : y = 1 : 6
Answer: 1:6Finance(150) Accounts (400) Student Total Internal Total Internal Percentage Marks Percentage Marks Percentage Marks Percentage Marks Sachin 25 37.5 10 4 25 100 10 10 Ashish 10 15 0 0 20 80 5 4 Tanwi 10 15 10 2 10 40 0 0 Ankit 5 7.5 10 1 10 40 10 4 Ramesh 20 30 10 3 30 120 25 30 Suresh 30 45 5 3 5 20 10 2 Incorrect
Sol. Option (A)
Let the total marks scored by all six students put together in Economics be ‘x’ and that in Accounts be ‘y’.
Then the total marks scored by Sachin in Economics = 30% of x
∴ Marks scored by Sachin in the internals of Economics = 20% of 30% of x = 0.06x
Similarly, the total marks scored by Ashish in Accounts = 20% of y
∴ Marks scored by Ashish in the internals of Accounts = 5% of 20% of y = 0.01y
From the condition given in the question, both these marks are equal.
∴ 0.06x = 0.01y
∴ x : y = 1 : 6
Answer: 1:6Finance(150) Accounts (400) Student Total Internal Total Internal Percentage Marks Percentage Marks Percentage Marks Percentage Marks Sachin 25 37.5 10 4 25 100 10 10 Ashish 10 15 0 0 20 80 5 4 Tanwi 10 15 10 2 10 40 0 0 Ankit 5 7.5 10 1 10 40 10 4 Ramesh 20 30 10 3 30 120 25 30 Suresh 30 45 5 3 5 20 10 2 
Question 91 of 100
91. Question
Category: Data InterpretationDirections for questions 9193:
China Exports (9899)= Rs. 14160353 m
USA
Europe
Asia
Others
Africa
Australia12%
4%
5%
7%40%
32%China Imports (9899)= Rs. 17609863 mn
USA
Australia
others
Africa
Asia
EuropeQ91. If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms
73% of import from Asia then trade balance of China as defined earlier with Korea is (approx.)Correct
Soln. Option (c)
Strategy Change the scale to minimize calculation
From both Import and Export figures, strike out the last 4 digits = 1750 & 1400 approximately
The answer options are far apart, therefore we can easily approximate.
China Imports (1750) Exports (1400) Asia (40%) 1750 x 40%=700 1400×40%=560 Korea (73%,80%) 700×73%= 511 560×80%= 448 Trade Deficit= Import Export = 511448≈63.
Point to note: You just need to check for the first digit of this question to arrive at the answer! Incorrect
Soln. Option (c)
Strategy Change the scale to minimize calculation
From both Import and Export figures, strike out the last 4 digits = 1750 & 1400 approximately
The answer options are far apart, therefore we can easily approximate.
China Imports (1750) Exports (1400) Asia (40%) 1750 x 40%=700 1400×40%=560 Korea (73%,80%) 700×73%= 511 560×80%= 448 Trade Deficit= Import Export = 511448≈63.
Point to note: You just need to check for the first digit of this question to arrive at the answer! 
Question 92 of 100
92. Question
Category: Data InterpretationQ92. If the foreign exchange reserves in the beginning of 199899 were Rs.11341 bn and Rs.2961 bn were withdrawn by Chinese residing abroad, then what will be the reserve at the end of year after adjusting trade deficit of the year?
Correct
Soln. Option (c)
Strategy Change the scale to minimize calculation (strike out the last 2 from billion figures and last 5 from million figures)
Trade Deficit for China= 175140 ≈35 billion
Initial foreign exchange reserve=11341
After withdrawal = 11329=84
After adjusting trade deficit, 8435 ≈49
Incorrect
Soln. Option (c)
Strategy Change the scale to minimize calculation (strike out the last 2 from billion figures and last 5 from million figures)
Trade Deficit for China= 175140 ≈35 billion
Initial foreign exchange reserve=11341
After withdrawal = 11329=84
After adjusting trade deficit, 8435 ≈49

Question 93 of 100
93. Question
Category: Data InterpretationQ93. The total import to China in 19981999 from Europe and Africa was nearly balanced by the total export from China to
Correct
Soln. Option (d)
Let us see how to apply this concept in this question
Total import to China from Europe and Africa = 39%
Factor of multiplication between the two charts= 176/141 ≈ 1.2
Thus, in the export chart, we need to look for 39 x 1.2 ≈ 48%
Look in the answer options
a) Asia, USA, Africa= 67%
b) Asia, Europe, Africa 71%
c) Europe, USA, Africa= 54%
d)Asia,others,Africa= 48%
Incorrect
Soln. Option (d)
Let us see how to apply this concept in this question
Total import to China from Europe and Africa = 39%
Factor of multiplication between the two charts= 176/141 ≈ 1.2
Thus, in the export chart, we need to look for 39 x 1.2 ≈ 48%
Look in the answer options
a) Asia, USA, Africa= 67%
b) Asia, Europe, Africa 71%
c) Europe, USA, Africa= 54%
d)Asia,others,Africa= 48%

Question 94 of 100
94. Question
Category: Data InterpretationDirection for questions 94 to 96 : Answer the questions based on the following table.
Market Share of company A in 4 Metropolitan Cities Period/Product Mumbai 1993 and 1994 Kolkata 1993 and 1994 Delhi 1993 and 1994 Chennai 1993 and 1994 HD 20 and 15 35 and 30 20 and 15 20 and 30 CO 20 and 25 30 and 15 15 and 10 20 and 15 BN 45 and 40 25 and 35 35 and 35 10 and 10 MT 15 and 20 10 and 20 10 and 10 50 and 45 Q94. The maximum percentage decrease in market share of any product in any city for company A is
Correct
Soln. Option (B)
From the table, the market share of CO in Kolkata has halved. It is the only product which shows such a drastic decrease in any city.
Hence, percentage of this decrease = 50%.
Incorrect
Soln. Option (B)
From the table, the market share of CO in Kolkata has halved. It is the only product which shows such a drastic decrease in any city.
Hence, percentage of this decrease = 50%.

Question 95 of 100
95. Question
Category: Data InterpretationQ95. The city in which the minimum number of products increased their market shares in 1993 to 94 is
Correct
Soln. Option (A)
It is clear from the table that the market shares only increased by two cities Mumbai and Kolkata, on the other hand, Chennai has 1, while Delhi has none.
So the answer is Delhi.
Incorrect
Soln. Option (A)
It is clear from the table that the market shares only increased by two cities Mumbai and Kolkata, on the other hand, Chennai has 1, while Delhi has none.
So the answer is Delhi.

Question 96 of 100
96. Question
Category: Data InterpretationQ96. The number of products which doubled their market shares in one or more cities is
Correct
Soln. Option (A)
From the given data in the table we can say that the market share is doubled for MT in Kolkata in 199394.So the answer is 1.
Incorrect
Soln. Option (A)
From the given data in the table we can say that the market share is doubled for MT in Kolkata in 199394.So the answer is 1.

Question 97 of 100
97. Question
Category: Data InterpretationDirection for questions 97 to 100 : Answer the questions based on the following table.
Students of 12^{th} standard of a school in Bangalore decided to take up online private coaching for Mathematics for a 3 month period starting from July. There are three institutes which provide online tutoring for class 12 students. The following information is available about the number of students who took up teaching services from these three institutes during the three months.
Students are allowed to switch from one institute to another only on the first of a month. They have to continue with that institute till the end of the month. A student is allowed to switch only once in a month. In any given month, a student is allowed to be with only one institute. 3 students switched from Edustar to Matonline at the beginning of August.The largest switch to any institute took place at the beginning of September when 11 students switched to Edustar
Q97. If no one switched from Gurumath to Edustar at the beginning of August and atleast one person switched to Gurumath at the beginning of August, what is the minimum number of people who should have switched out of Matonline at the beginning of August?
Correct
Solution: Option (b)
3 students moved out of Edustar in the beginning of August, and the total people tutoring at Edustar in August has increased to 36. So, atleast 9 students have shifted to Edustar atthe beginning of august. The one addition to Gurumath could have been from Edustar orMatonline.
CASE 1 If it had been from Matonline, then 9 students have switched to Edustar at the beginning of August. As no one shifted to Edustar from Gurumath,the entire 9 should have shifted out of Matonline and one person who shifted to Gurumath should have also been from Matonline, so minimum=10
CASE 2 If the one addition to Gurumath had been from Edustar, then 4 students would have shifted out of Edustar and hence, 10 students should have shifted to Edustar at the beginning of august. As no one shifted from Gurumath to Edustar, a minimum of 10 people should have shifted out of Matonline.
Incorrect
Solution: Option (b)
3 students moved out of Edustar in the beginning of August, and the total people tutoring at Edustar in August has increased to 36. So, atleast 9 students have shifted to Edustar atthe beginning of august. The one addition to Gurumath could have been from Edustar orMatonline.
CASE 1 If it had been from Matonline, then 9 students have switched to Edustar at the beginning of August. As no one shifted to Edustar from Gurumath,the entire 9 should have shifted out of Matonline and one person who shifted to Gurumath should have also been from Matonline, so minimum=10
CASE 2 If the one addition to Gurumath had been from Edustar, then 4 students would have shifted out of Edustar and hence, 10 students should have shifted to Edustar at the beginning of august. As no one shifted from Gurumath to Edustar, a minimum of 10 people should have shifted out of Matonline.

Question 98 of 100
98. Question
Category: Data InterpretationQ98. If no one shifted to Gurumath and if noone switched from Gurumath to Edustar at the beginning of August,
Which of the following is correct?
 The percentage of students shifting out of a tutoring service as a percentage of the students at the beginning of the previous month was highest at the beginning of August for Matonline.
 The number of students who shifted out of Edustar is the same as those who shifted out of Gurumath at the beginning of August
Correct
Solution : Option (b)
If noone shifted to Gurumath at the beginning of august, then 3 have shifted out of Gurumath and these 3 should have gone to Matonline as noone shifted from Gurumath to Edustar. So, a total of 9 students have shifted out of Matonline, 3 out of Gurumath and 3 out of Edustar at the beginning of august. As a percentage, Edustar at 10% is the highest. Hence only statement II is true
Incorrect
Solution : Option (b)
If noone shifted to Gurumath at the beginning of august, then 3 have shifted out of Gurumath and these 3 should have gone to Matonline as noone shifted from Gurumath to Edustar. So, a total of 9 students have shifted out of Matonline, 3 out of Gurumath and 3 out of Edustar at the beginning of august. As a percentage, Edustar at 10% is the highest. Hence only statement II is true

Question 99 of 100
99. Question
Category: Data InterpretationQ99. If at the beginning of September no one shifted between Matonline and Gurumath, what is the minimum number of students who shifted from Gurumath to Edustar at the beginning of September?
Correct
Solution: Option (c)
If 11 students shifted to Edustar at the beginning of September, and the total students tutoring at Edustarhas increased only by 7, then 4 students shifted out of Edustar at the beginning of September. Of these, atleast one should have shifted to Gurumath as its total number has increased to 39 from 38. the remaining 3 could have shifted to Matonline. So a minimum of no students needed to have shifted from Gurumath to Edustar
Incorrect
Solution: Option (c)
If 11 students shifted to Edustar at the beginning of September, and the total students tutoring at Edustarhas increased only by 7, then 4 students shifted out of Edustar at the beginning of September. Of these, atleast one should have shifted to Gurumath as its total number has increased to 39 from 38. the remaining 3 could have shifted to Matonline. So a minimum of no students needed to have shifted from Gurumath to Edustar

Question 100 of 100
100. Question
Category: Data InterpretationQ100. Which of the following is correct if no one shifted between Matonline and Gurumath at the beginning of September?
I) One student shifted out of Gurumath at the beginning of September
II) 2 students shifted to Matonline
Correct
Solution: Option (a)
We know that 4 students have shifted out of Edustar. If one student shifts out of Gurumath (Assuming statement I as true) and the strength of Gurumath has increased to 39, then 2 students have shifted to Gurumath. As no one shifted between Gurumath and Matonline, the remaining 2 students out of Edustar should have shifted to Matonline. So statement II is provided statement I is true.
Incorrect
Solution: Option (a)
We know that 4 students have shifted out of Edustar. If one student shifts out of Gurumath (Assuming statement I as true) and the strength of Gurumath has increased to 39, then 2 students have shifted to Gurumath. As no one shifted between Gurumath and Matonline, the remaining 2 students out of Edustar should have shifted to Matonline. So statement II is provided statement I is true.