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Q 1. The number of factors of 360 is:
- 30
- 12
- 24
- 15
Answer: B
Solution 1: 360 = 2^{3 }* 3^{2} * 5^{1}
Hence number of factors = (3+1) * (2+1) * (1+1)
= 4 * 3 * 2
= 24
Q 2. Find the sum of factors of 40
- 80
- 90
- 75
- 60
Answer: B
Solution 2:
40 = 2^{3 }× 5^{1}
Sum of factors = [(2^{(3+1)} – 1) × (5^{(1+1)} – 1)] / [ (2-1) × (5-1) ]
= (15 × 24) / (1 × 4)
= 90
Q 3. Total number of odd factors of 75 is
- 8
- 10
- 12
- 16
Answer: A
Solution 3:
75 = 5^{3} × 3^{1}
Hence number of odd factors = (3+1)× (1+1)
= 8
Q 4. If p! – p = p, then the value of p is:
- 3
- 5
- 2
- 7
Answer: A
Solution 4:
Best way to solve this question is through options
3! – 3 = 6-3 =3
Q 5. If a, b are the positive integers (b> 1) such that a^{ b} = 121, then the value of (a – 1) ^{b+1} is
- 1200
- 1000
- 1500
- 2000
Answer: B
Solution 5:
We can see that, a^{b} = 121
b>1
Hence (11)^{2 }= 121
a= 11, b=2
(a – 1) ^{b+1} = (11-1) ^{2+1} = 10^{3 } = 1000
Q 6. Find the number of rectangles in the following figure
- 45
- 100
- 80
- 35
Answer: B
Solution 6
Logic: Number of rectangles in a square of side n * n side = 1^{3 }+ 2^{3} + 3 ^{3 }+…..+n ^{3}
Hence, in the above question
1^{3} + 2^{3} + 3^{3} + 4^{3} = 1 + 8 + 27 + 64 = 100 rectangles
Q 7. Divide 120 into 3 parts such that first part be double that of second part and the second part be (⅓)^{rd} of the third part. What is the third part?
- 60
- 50
- 25
- 100
Answer: A
Solution 7:
A:B = 2:1
B:C= 1:3
A:B:C = 2:1:3
C = 120 × (3/6) = 60
Q 8: Find the units digit of the expression:27 × 32 × 46 × 54 × 17 × 21 × 63
- 7
- 6
- 8
- 9
Answer: B
Solution 8:
27 × 32 × 46 × 54 × 17 × 21 × 63
The units digit of an expression can be calculated by getting the remainder while the expression is divided by 10.
Hence, we try to find the remainder
= (27 × 32 × 46 × 54 × 17 × 21 × 63) / 10
Remainder of 27/10 = 7
Remainder of 32/10 = 2
Remainder of 46/10 = 6
Remainder of 54/10 = 4
Remainder of 17/10 = 7
Remainder of 21/10 = 1
Remainder of 63/10 = 3
Hence, we find remainder of (7 × 2 × 6 × 4 × 7 × 1 × 3) / 10
Remainder of (14 × 24 × 21) / 10
Remainder of 14/10 = 4
Remainder of 24/10 = 4
Remainder of 21/10 = 1
Hence we find remainder of (4×4×1)/10 = Remainder of 16/10 = 6
Hence the unit digit of the expression 27 × 32 × 46 × 54 × 17 × 21 × 63 = 6
Shorter method: Directly find the Units digit by multiplying 7 × 2 × 6 × 4 × 7 × 1 × 3 and only accounting for Units digit.
Q 9. Find the unit digit of (52)^{97} × (73)^{72}
- 2
- 4
- 6
- 8
Answer: A
Solution 9: Find the unit digit of 2^{97} * 3^{72}
= 2^{4(24)} * 2
Unit digit of 2^{4} = 6
Unit digit of 6 * 2 = 2
= 3^{4(24)}
Unit digit of 3^{4} = 1
Hence unit digit of expression = 2 * 1 = 2
Directions (10-14):
7 persons namely A, B, C, D, E, F and G visit a movie palace having 3 screens (Screen 1,2, and 3). Each of them studies different courses namely MCA, BCA, MBA, BBA, BE, B.Tech, and M.Tech, but not necessarily in the same order. Out of these, 2 persons are watching a movie on screen 1, three are watching on screen 2, and two are watching on screen 3.
A studies MCA but is not watching the movie on screen 3. The person, who studies MBA, is the only one, who is watching the movie on the same screen, in which A is watching. B and F are not watching the movie on screen 2, and they study M.Tech and BE respectively. C studies BBA. G neither studies MBA nor B.Tech. The person E is watching the movie on the same screen, in which the person who studies at BCA is watching.
Q 10. Which course does D study?
- BBA
- B.Tech
- MBA
- BE
- MCA
Answer: C
According to the information given, the relationship between persons, courses and screens are shown in the table.
Solution 10
Person | Course | Movie Screen |
A | MCA | Screen 1 |
B | M.Tech | Screen 3 |
C | BBA | Screen 2 |
D | MBA | Screen 1 |
E | B.Tech | Screen 2 |
F | BE | Screen 3 |
G | BCA | Screen 2 |
Q 11. Who studies BCA?
- B
- C
- D
- A
- G
Answer: E
Solution 11:
From the above table, we can find that G studies BCA
Q 12. Which of the following group of persons is watching a movie on screen 2?
- C, D and E
- G, D and C
- D, E and C
- G, C and E
- E, G and D
Answer: D
Solution 12.
From the above table, we can find G, C and E are watching the movie on screen 2.
Q 13. Which of the following is the correct combination?
- B – MCA – Screen 2
- C- BBA – Screen 2
- G – B.Tech – Screen 3
- F – BE- Screen 2
- B – BCA – Screen 1
Answer: B
Solution 13:
From the above table, we can find that correct combination is C-BBA-Screen 2.
Q 14. Who studies M.Tech and is watching a movie on screen 3?
- B
- G
- E
- F
- A
Answer: B
Directions (15-19):
7 friends P, Q, R, S, T, U and V are studying different subjects, such as Hindi, English, Physics, Biology, Science, Maths and Chemistry, but not necessarily in the same order. All of them attend different lectures on various days a week from Monday to Sunday. Out of the seven, there are three female members.
R is the sister of T, studies biology and attends the lecture on Wednesday. T, the wife of U, studies Physics and attends the lecture on Friday. One who studies English attends the lecture on Tuesday and is also a female member. Q and U attend the lectures on Tuesday and Saturday respectively. One who attends the lecture on Sunday studies Science. P attends the lecture on Monday but the subject is neither Hindi nor Physics. S attends the lecture on Chemistry on Thursday.
Q 15. —— attends the lecture on Tuesday and —— attends the lecture on Sunday.
- V; Q
- Q; P
- V; U
- P; Q
- None of these
Answer: E
Solution 15:
Day | Person | Gender | Subject |
Monday | P | Male | Maths |
Tuesday | Q | Female | English |
Wednesday | R | Female | Biology |
Thursday | S | Male | Chemistry |
Friday | T | Female | Physics |
Saturday | U | Male | Hindi |
Sunday | V | Male | Science |
From the table, we can see that Q attends the lecture on Tuesday and V on Sunday.
Q 16. Who represents the group of female members?
- P, Q and R
- R, T and V
- Q, R and U
- Q, R and T
- Other than given options
Answer: D
Solution 16:
According to the table, Q, R and T represent the group of female members.
Q 17. P attends the lecture of —— on ——-
- Maths, Tuesday
- Hindi, Saturday
- English, Tuesday
- Hindi, Friday
- Maths, Monday
Answer: E
Solution 17:
According to the table, P attends the lecture of Maths on Monday.
Q 18. Who attends the lecture of Hindi?
- U
- V
- Q
- Either (1) or (2)
- Other than given options
Answer: A
Solution 18:
According to the arrangement, U attends the lecture of Hindi on Saturday.
Q 19. Lecture of ——- was arranged on Monday and lecture of ——- was arranged on Saturday.
- Hindi, Maths
- Maths, Science
- Hindi, English
- Biology, Chemistry
- Other than given options
Answer: E
Solution 19:
According to the arrangement, the lecture of Maths is arranged on Monday and lecture of Hindi is arranged on Saturday.
Directions (20-24):
Rearrange the following sentences P, Q, R, S, T, U and V in a proper sequence so as to form a meaningful paragraph, then answer the questions given below them. The paragraph starts with the sentence P and ends with the sentence V. The positions of both P and V are fixed.
P. An earthquake rocked Indonesia in September 2018. More than 4000 peoples lives were lost and it is estimated that over 600 people were missing. Most of the people lost their lives having been buried under the debris of buildings that collapsed.
Q. Heat is continuously produced in the depths of the earth. The resultant heat produces convection currents in the molten rocks.
R. As the current rises unabated, it causes fractures in the crust. The crust is divided into various segments.
S. These segments have been continuously moving away from each other and then moving towards each other. As the plates move towards each other, they start colliding.
T. The earthquake had its epicentre at Minahasa Peninsula in the region of Sulawesi. Most of the damage was caused in the immediate surroundings of the epicentre.
U. An earthquake is caused by vibration generated in Earths crust.
V. The stress caused by collision causes leads to vibration of the earth’ crust. We call this shaking and trembling of the surface of the earth as Earthquake.
Q 20. Which of the following should be the sixth sentence?
- Q
- S
- R
- U
- T
Answer: B
Q 21. Which of the following should be the fourth sentence?
- R
- T
- U
- S
- Q
Answer: E
Q 22. Which of the following should be the fifth sentence?
- Q
- R
- T
- S
- U
Answer: B
Q 23.Which of the following should be the second sentence?
- U
- Q
- T
- R
- S
Answer: C
Q 24. Which of the following should be the third sentence?
- R
- S
- Q
- U
- T
Answer: D
Q 25. What is the Synonym of the word mentioned in the bold
Obdurate
- Stubborn
- Amenable
- Malleable
- Tractable
Answer: A
Q 1. 2 alarm clocks ring their alarms in at regular intervals of 60 seconds and 40 seconds. If they first beep together at 1 noon, at what time will they beep again.
- 1:20 PM
- 1:02 PM
- 1:05 PM
- 1:40 PM
Answer: B
Solution 1: LCM of 60 and 40 is 120. The 2 clocks will ring again after 120 seconds.
Q 2. 3 bells toll together at 10:00 AM. They toll after 6, 8,10 seconds respectively. How many times will they toll together again in the next 1 hour?
- 30
- 15
- 25
- 40
Answer: A
Solution 2: LCM of 6, 8, 10 is 120.
No of time they will toll together in 1 hour = (3600/120) = 30 times
Q 3. On MG Road, 3 consecutive traffic lights change after 20, 40 and 72 seconds. If the lights are switched on at 10:00 AM, at what time will they change simultaneously?
- 10: 05 AM
- 10:10 AM
- 10:06 AM
- 11:00 AM
Answer: C
Solution 3: The LCM of 20,40 and 72 seconds is 360.
Hence 360/60 = 6 minutes.
They will change simultaneously after 6 minutes.
Q. 4 2 equilateral triangles have sides of lengths 32 m and 80 m respectively. The greatest length of tape that measure both of them exactly is?
- 16
- 24
- 8
- 7
Answer: A
Solution 4: HCF of 32 and 80 is 16 m.
Hence the greatest length of tape that can measure both of them is 16 m.
Q 5. 2 varieties of rice at Rs 10/kg and Rs 15/kg are mixed in the ratio 3:2. Find the average price of the resulting mixture.
- 12
- 15
- 20
- 16
Answer: A
Solution 5:
(3/2) = (15-A_{w}) / (A_{w }– 10)
3 A_{w} – 30 = 30 – 2 A_{w}
5 A_{w} = 60
A_{w} = Rs 12/Kg
Q 6. If a varies inversely as b^{3} – 1 and is equal to 3 when b=2, find a when b=4
- ⅓
- ¼
- ⅔
- 1
Answer: A
Solution 6:
a= k/(b^{3} – 1)
k= 3 * 7 = 21
When b= 4, equation becomes a = 21/ (4^{3} – 1)
= 21/63 = 1/3
Q 7. If a varies as b, and b=4 when a=12, find a when b = 15
- 65
- 46
- 45
- 10
Answer: C
Solution 7:
a= kb
12= 4k
k=3
Hence, a= 3 * b
When b= 15, a= 3 * 15 = 45
Q 8. If a varies as b directly, and as c inversely, and a=12, when b=3, find c when a=4, b=5
- ½
- 1/7
- ¾
- Cannot determine
Answer: D
Solution 8:
a=kb/c
We cannot determine the value of k from the given information and hence cannot answer the question.
Q 9. If 3a^{2} + 3b^{2} = 10 ab, what is the ratio of a to b?
- 1:4
- 4:1
- 1:3
- 3:1
Answer: C
Solution 9:
Short cut Tip: Use options to solve the problem
Direction (10-11): Solve the analogy
Q 10. Plumber: Wrench
- Captain: Ship
- Loco Pilot: train
- Carpenter: Hammer
- Pilot: Airplane
Answer: C
Solution 10:
The plumber uses a wrench as a tool. Carpenter uses a hammer as a tool. In the rest of the options captain, loco pilot, the pilot does not use them as a tool to finish a job.
Q 11. Fencing: Sabre
- Shooting: Pistol
- Archery: Recurve
- Baseball: Bat
- Judo: Ippon
Answer: D
Solution 11:
Judo is just a hand combat sport, equipment is not used in this sport.
Directions (12-16): Choose the synonyms of the words given in Bold.
Q 12. Connoisseur
- Canonise
- Callow
- Ghastly
- An expert judge of
Answer: D
Q 13. Bulwark
- Bucolic
- Brusque
- Burnish
- A Defence
Answer: D
Q 14. Cabal
- A group of plotters
- A group of immature
- Cadence
- Resonant
Answer: A
Q 15. Cozen
- To cheat
- Counterbalance
- Contingent
- Outward behaviour
Answer: A
Q 16. Console
- Give comfort
- Despise
- Guesswork
- Discordant
Answer: A
Directions (17-18): Fill in the blanks with appropriate word
Q 17. Government of India decided to ————— Article 370
- Abandon
- Abrogate
- Accede
- Exceed
Answer: B
Q 18. Garibaldi, meanwhile, met his former hero Mazzini for the first time, and again the encounter was ——–
- Frosty
- Convivial
- Genial
- Affable
Answer: A
Directions (19-22):
Study the following information carefully and answer the questions given below:
J, K, L, M, N, O, P and R are sitting around a circular table facing the centre. Each of them was born in a different year – 1971, 1975, 1979, 1980, 1981, 1984, 1985, and 1990; but not necessarily in the same order.
M is sitting to the right of K. L is sitting third to the right of J. Only the one born in 1984 is sitting exactly between J and K. N, who is the eldest is not an immediate neighbor of J and M. R is older than only M. R is sitting second to the left of P. P is not an immediate neighbor of N. J is younger than L and O. K was born before O, but he is not the second eldest.
Q 19. Who is the second eldest in the group?
- J
- L
- K
- P
- O
Answer: B
Solution 19:
Q 20. Who is sitting third to the right of O?
- The one born in 1979
- The one born in 1980
- The one born in 1985
- The one born in 1984
- The one born in 1985
Answer: E
Solution 20:
From the figure, J is sitting third to the right of O. J was born in 1985.
Q 21: In which year was R born?
- 1979
- 1975
- 1980
- 1985
- 1981
Answer: D
Q 22. Which of the following statements is true regarding K?
- K is sitting third to the right of R.
- The one who was born in 1975 is to the immediate left of K.
- K is younger than R
- There are 4 people sitting between N and K
- K sits to the immediate right of J
Answer: A
Directions (23-25): In each of the following questions, various terms of an alphabet series are given with one or more terms missing as shown by (?). Choose the missing terms out of the given alternatives.
Q 23. V, C, J, Q, X,?
- E
- F
- Q
- Z
Answer: A
Solution 23:
V –+7 —> C —+7—-> J —+7—-> Q—+7—> X—+7—>E
Q 24. BZ, DX, GU,?
- IR
- IV
- KQ
- KP
Answer: C
Solution 24:
1st letter: B —+2—> D—+3—>G—+4—>K
2nd letter: Z–(-2) —>X—(-3)—>U–(-4)–>Q
Q 25. PME, OOD, NQC, MSB,?
- LUA
- LVP
- LVR
- LWP
Answer: A
Solution 25:
1st letter: P –(-1)–> O –(-1)–N–(-1)–>M–(-1)–>L
2nd letter: M –(+2)–>O–(+2)–>Q–(+2)–>S–(+2)–>U
3rd letter: E–(-1)–>D—(-1)–>C–(-1)–>B–(-1)–>A
Directions Q. (1-3): In each of the following questions, relationship between different elements is shown in the statements. The statements are followed by two conclusions numbered I and II. Study the conclusions based on the given statements and mark the appropriate answer as :
a. If both conclusion I and conclusion II are true
b. If neither conclusion I nor conclusion II is true
c. If only conclusion I is true
d. If only conclusion II is true
e. If either conclusion I or conclusion II is true
Q. (1) Statement: A ≥ B > C < D = E > F; G < F; H < I
Conclusions:
I. C < F
II. H > G
Answer: c (only conclusion I is true)
Solution 1: From the given statement A ≥ B > C < D = E > F; G < F; H < I, we get
· A > C
· C < E but E > F, therefore, C < F
· Thus, conclusion II is incorrect
Q. (2) Statement: P < Q = R ≤ S < T ≤ U = V; W < S ≥ X
Conclusions:
I. P < S
II. Q > X
Answer: c (only conclusion I is correct)
Solution: From the given statement P < Q = R ≤ S < T ≤ U = V; W < S ≥ X, we get
· P < S
· Also, S < T ≤ U = V. Therefore, P < V
· W < X
· Therefore, only conclusion I is correct.
Q. (3) Statement: R < A = I ≥ N; S ≥ A
Conclusions:
I. S > N
II. N = S
Answer: e (either conclusion I or conclusion II is correct)
Solution: From the given statement R < A = I ≥ N; S ≥ A, we get
· S ≥ A, but A = I and I ≥ N, therefore, S > N or S = N
· Thus, either conclusion I or conclusion II is correct
Q. (4) In a class of 45 students, Ayushi’s rank is fourth from the top. Megha is five ranks below Ayushi. What is Megha’s rank from the bottom?
a. 33
b. 37
c. 14
d. 17
e. 25
Answer: b
Solution: Total number of students in the class = 45
Megha’s rank from the top = (Ayushi’s rank from the top + 5) = 4 + 5 = 9
Megha’s rank from the bottom = (Total number of students in the class – Megha’s rank from the top) + 1 = (45 – 9) + 1 = 37
Directions Q. (5-6): Each of the questions below consist of two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Mark your answer as:
a. If the data in statement I are alone sufficient
b. If the data in statement II are alone sufficient
c. If the data in either statement I or in statement II are sufficient
d. If the data in both statements I and II are not sufficient
Q.(5) A, B, C, D and E are sitting around a circular table facing the centre, such that there is equal space between each of the adjacent members. Who sits to the immediate right of E?
I. B sits second to the right of E and D sits second to the left of E.
II. C is not an immediate neighbour of either A or B.
Answer: d (The data in both statements I and II are not sufficient)
Solution: The seating arrangement that we can assume from both the statements are mentioned in the image below:
Thus, we can assume that A sits immediate right of E.
Therefore, the data provided in the statements are not sufficient to answer the question.
Q. (6) Which direction is Raunaq facing at the moment?
- After walking 6 metres early in the morning from point X, Raunaq is facing the opposite direction of the sun.
- Rauanq took four consecutive left turns after covering a distance of 5 metres to reach point A.
Answer: a (The data in statement I are alone sufficient)
Solution:
Directions Q. (7-8): Five boxes P, Q, R, S and T are kept above one another. Each box is of different colour i.e., Orange, Red, Yellow, Purple and Green. The yellow box is kept immediately above S. Only two boxes are kept between the orange and the red boxes. The orange box is kept at one of the positions above the red box as well as S. More than one box is kept between the red box and P. P is not orange in colour. As many boxes are kept between P and the yellow box as between R and the purple box, S is not purple in colour. Q is kept at one of the positions below the orange box but not immediately below it.
Q. (7) How many boxes are kept between T and the green box?
a. Three
b. One
c. Two
d. Four
e. None of the above
Answer: b
Q. (8) Which of the following represents the colour T?
- Yellow
- Purple
- Green
- Red
- Orange
Answer: e
Solution Q.(7-8):
Box | Colour |
Box P | Purple |
Box T | Orange |
Box R | Yellow |
Box S | Green |
Box Q | Red |
Box S is green in colour and only one box is kept between T and S.
Directions Q. (9-11): In each of the following questions, one or two equations is/are given. On the basis of these equations, you have to determine the relation between m and n. Mark your answer as:
a. If m < n
b. If m > n
c. If m ≤ n
d. If m ≥ n
e. If m = n
Q. (9) I. m^{2}+ 3m + 2 = 0
II. 2n^{2 }= 5n
Answer: a (m < n)
Solution: From statement I, m^{2} + 2m + m + 2 = 0
⇐ m (m+2) + 1 (m+2) = 0
⇐ (m+1) (m+2) = 0
∴ m = -1 or m = -2
From statement II, 2n^{2 }– 5n = 0
⇐ n (2n – 5) = 0
∴ n = 0 or n = 5/2
Conclusion: m < n
Q. (10) I. n^{2} + 2n – 3 = 0
II. 2m^{2 }– 7m + 6 = 0
Answer: b (m > n)
Solution: Statement I ⇒ n^{2 }+ 3n – n – 3 = 0
⇐ n (n + 3) – 1 (n + 3) = 0
⇐ (n – 1) (n + 3) = 0
∴ n = 1 or n = -3
Statement II ⇒ 2m^{2 }– 4m – 3m + 6 = 0
⇐ 2m (m – 2) -3 (m – 2) = 0
⇐ (m – 2) (2m – 3) = 0
∴ m = 2 or m = 3/2
Thus, m > n
Q. (11) I. m^{2} – 5m + 6 = 0
II. n^{2} + n – 6 = 0
Answer: d (m ≥ n)
Solution: Statement I ⇒ m^{2 }– 3m – 2m + 6 = 0
⇐ m (m – 3) – 2 (m – 3) = 0
⇐ (m – 3) (m – 2) = 0
∴ m = 3 or m = 2
Statement II ⇒ n^{2} + 3n – 2n – 6 = 0
⇐ n (n + 3) – 2 (n + 3) = 0
⇐ (n + 3) (n – 2) = 0
∴ n = -3 or n = 2
Thus, m ≥ n
Directions Q. (12-15): What will come in place of (?) in the following number series?
Q. (12) 9.57, 17.63, 29.12, 43.86, (?)
a. 61.83
b. 61.63
c. 57.13
d. 57.63
e. 59.83
Answer: a
Solution: The pattern of the series is:
· [5 + (3.5)^{3}] / 5 = 9.57
· [10 + (5.5)^{3}] / 10 = 17.63
· [15 + (7.5)^{3}] / 15 = 29.12
· [20 + (9.5)^{3}] / 20 = 43.86
· [25 + (11.5)^{3}] / 25 = 61.83
Q. (13) 42.8, 166.3, 421.8, 857.3, (?)
a. 1525
b. 1057.8
c. 1520.8
d. 1520.3
e. None of the above
Answer: c
Solution: The pattern of the series is
· [5 ✕ (3.5)^{3}] / 5 = 9.57
· [10 ✕ (5.5)^{3}] / 10 = 17.63
· [15 ✕ (7.5)^{3}] / 15 = 29.12
· [20 ✕ (9.5)^{3}] / 20 = 43.86
· [25 ✕ (11.5)^{3}] / 25 = 61.83
Q. (14) 3.5, 3.6, 4.5, 5.42, (?)
a. 4.6
b. 5.6
c. 6.38
d. 6.6
e. 7.3
Answer: c
Solution: The pattern of the series is:
· [5 ✕ (3.5)] / 5 = 3.5
· [10 ✕ (5.5)] / 15 = 3.6
· [15 ✕ (7.5)] / 25 = 4.5
· [20 ✕ (9.5)] / 35 = 5.42
· [25 ✕ (11.5)] / 45 = 6.38
Q. (15) 96.3, 72.2, 63, 58.7, (?)
a. 52.2
b. 56.8
c. 46.2
d. 46.8
e. 46.3
Answer: b
Solution: The pattern of the series is:
· (17)^{2} / 3 = 289 / 3 = 96.3
· (19)^{2 }/ 5 = 361 / 5 = 72.2
· (21)^{2} / 7 = 441 / 7 = 63
· (23)^{2 }/ 9 = 529 / 9 = 58.7
· (25)^{2} / 11 = 625 / 11 = 56.8
Q. (16) A shopkeeper sold a book for Rs.640 and earned a profit of 25%. At what price should it be sold so as to earn a profit of 30%?
a. 670
b. 680
c. 720
d. 665.6
e. 700
Answer: d
Solution: According to the question,
Cost price of the book = [100/ (100 + gain %)] x selling price
= (100/125) x 640
= Rs. 512
Hence, required selling price = [(100 + gain %) /100] x cost price
= (130/100) x 512
= Rs. 665.6
Q. (17) 42 men can complete a work in 8 days and 22 women can complete the same work in 16 days. What is the respective ratio between the amount of work done by 34 men in 4 days and amount of work done by 36 women in 5 days?
- 17/21: 45/44
- 16/21: 45/37
- 89: 57
- 11/15: 4/13
- 21/17: 44/45
Answer: a
Solution: Let W_{1 }and W_{2 }be the first and second set of work respectively.
According to the question,
Total number of men required to finish the first set of work (M_{1}) = 42
Number of days taken by 42 men to complete the first set of work (D_{1}) = 8
Total number of men required to finish the second set of work (M_{2}) = 34
Number of days taken by 34 men to complete the second set of work (D_{2}) = 4
∴ (M_{1 }x D_{1}) / 1 = (M_{2} x D_{2}) / W_{2}
⇐ 42 x 8 = (34 x 4) / W_{2}
⇐ W_{2} = 136 / 336
⇐ W_{2} = 17 / 42
Now, the total number of women required to finish the first set of work (N_{1}) = 22
Number of days taken by 22 women to complete the first set of work (E_{1}) = 16
Total number of women required to finish the second set of work (N_{2}) = 36
Number of days taken by 36 women to complete the second set of work (E_{2}) = 5
∴ (N_{1 }x E_{1}) / 1 = (N_{2} x E_{2}) / W_{2}
⇐ 22 x 16 = (36 x 5) / W_{2}
⇐ W_{2} = 180 / 352
⇐ W_{2} = 45 / 88
∴ Required ratio = 17/42: 45/88
= 17/21: 45/44
Q. (18) Given below are five sentences or parts of sentences that form a paragraph. Identify the sentence (s) or parts of sentences(s) that is/are incorrect in terms of grammar and usage. Then choose the correct option.
A. India’s Queen of the Arabian Sea, Kochi, is an example of the core issues that prevent exporters in exploiting rupee weakness.
B. The city is rife with power cuts, so manufacturers are forced to rely on expensive onsite generation.
C. The Kochi Port is so congested that trucks often spend three days driving just 30kms from the factory district to the port
D. A long-proposed expressway is delayed.
E. The boom period during the last decade is not matched by increased infrastructure, so traders struggled to get their products to cargo ships on time.
a. ABC
b. ADC
c. BCD
d. BDE
e. ACD
Answer: e (Sentences A, C and D are correct)
Q. (19) In the paragraph given the last sentence has been deleted. From the options given below, choose the one that completes the paragraph in the correct way.
By creating a sense of equality, socialism was supposed to eliminate human envy. But instead, the opposite happened. It so happens that as the social level increases, so does the envy. This is what happened in the Soviet Union, where even tiny differences, such as new curtain holders, were exaggerated in the neighbours’ eyes.__________
a. Envy is felt more strongly by those far below the social ladder than those who are near equals.
b. In this, there is more than a hint of the general envy of the have-nots for the rich.
c. Socialist societies, however, turned out to be one of the most envious.
d. If greed is the vice of capitalism, then envy is the flaw of socialism.
Answer: (d) If greed is the vice of capitalism, then envy is the flaw of socialism.
Solution: Option (d) is the right answer as it correctly sums up the main idea of the paragraph.
Q. (20) Five sentences are given below labelled A, B, C, D and E. They need to be arranged in a logical order to form a coherent paragraph/passage. From the given options, choose the most appropriate one.
A. Against West Indies last year he became the second skipper in history to win the match after declaring behind in the first innings.
B. Watson dismissed Alastair Cook, and Hussey once got Kumar Sangakarra when he was well set.
C. In a different match against Sri Lanka, Clarke even gave the ball, only 10 overs old at the time to his wicketkeeper Matthew Wade.
D. Tactically, he is the most innovative and exciting captain to play Test cricket since Stephen Fleming retired.
E. Then there are his gunshot bowling changes, the single over he gave Shane Watson early on at Lord’s, a trick he often played with Hussey when he was still in the side.
a. ACDEB
b. DABEC
c. DAEBC
d. ADEBC
Answer: (c) DAEBC
Q. (21) Four sentences are given below labelled A, B, C and D. Of these, three sentences need to be arranged in a logical order to form a coherent paragraph/passage from the given options, and the other one is not part of the sequence. Choose the odd one amongst the four sentences.
A. Everywhere they created gardens large and small, private and public that embodied their aesthetic ideals and philosophical understanding of useful life of civilisation and political order.
B. Gardens gave the British enough opportunity to set an example of ‘civilized’ life for the ‘natives’.
C. Well kept gardens with manicured lawns and flower beds were a means of distancing oneself from the smells and dirt of India.
D. Maintaining a garden was one of the ways that a person could establish himself as a member of the ruling elite, distinct from the indigenous society.
a. A
b. B
c. C
d. D
Answer: (a) Everywhere they created gardens large and small, private and public that embodied their aesthetic ideals and philosophical understanding of useful life of civilisation and political order.
Solutions: Option (a) is the most neutral and the correct answer as it is a rather general statement, unlike the other comments which refer to British superiority and distinction through their gardens.
Q. (22) There are two gaps in the sentence/paragraph given below. Choose from the pair of words given below that will fill the gaps most aptly.
Beneath the rolling______ is a nation possessed by an almost_______eagerness to rejoin the free world.
a. Sureties, unnatural
b. certainties, unquenchable
c. uncertainties, adolescent
d. certainty, remarkable
Answer: (c) uncertainties, adolescent
Q. (23) In the paragraph given below, the last sentence has been deleted. From the options given below, choose the one that completes the paragraph accurately.
When India revised its policy with regards to foreign investment, the country’s balance of payments difficulties had not been resolved. However, the assumption was that foreign firms would use India as a base for world market production, earning the country, vast amounts of foreign exchange. However, such expectations have been dashed.__________.
a. This makes the foreign exchange cost of liberalization high, with an adverse effect on the balance of payments.
b. Foreign firms do not engage in export, but their main focus is always the domestic market.
c. In order to limit foreign presence, the government in those years resorted to regulation to reduce the cost of foreign presence.
d. That experience suggested that policy favouring foreign capital partly explained India’s haphazard growth
Answer: (b) Foreign firms do not engage in export, but their main focus is always the domestic market.
Solution: Option (b) is correct as it explains why expectations in foreign investments were dashed.
Q. (24) Four sentences are given below labelled (a), (b), (c) and (d). Of these, three sentences need to be arranged in a logical order to form a coherent paragraph/passage from the given options, the one that is not part of the sequence.
a. The general theme of the debate is the validity of Western writings of the 18th and 19th centuries – specifically, that of the Enlightenment thought – to the rest of the world.
b. The post-colonial literature refers to writings resulting from these reflections and include diverse branches such as philosophy, politics, economics, and so on.
c. The emergence of a large number of ex-colonies, as independent countries after World War II, provided the opportunity for thinkers and writers to reflect on the experience of the colonial era.
d. The common essence of these writings is that the imperialist era had a mindset similar to that of life in the “West” and since life in the colonies were poles apart different ways of thinking was called for.
Answer: a (The general theme of the debate is the validity of Western writings of the 18th and 19th centuries – specifically, that of the Enlightenment thought – to the rest of the world.)
Solution: Rather than talking about colonial writings in particular, option (a) talks about the theme of a debate on the issue of the relevance of western thought and writings in general. Thus this sequence does not fit into the answer.
Q. (25) A constitutional monarchy or republic was the de facto political institution of the moderate or small nations of Europe, ______, the rule by fear of an all-powerful autocrat over a docile and servile populace, is the normal and distinctive political institution of the East during the middle ages.
a. Democracy, tyrannical
b. nepotism, centrist
c. dictatorship, reformist
d. despotism, capricious
Answer: (d) despotism, capricious
Q. (1) The following paragraph has one italicised bold word that does not make sense. Choose the most appropriate replacement for that word, from the options given below the paragraph.
Neither sociologists nor economists have been happy with the wide usage of the term ‘social capital’ the former because they see it as an infringement of the social sciences by economics and the latter because they regard it as a matistic concept that is difficult to measure.
- Recondite
- Abstruse
- Nebulous
- Arcane
Answer: (c) nebulous
Q. (2) In the following question, the word given in capital letters is used in four different ways numbered a to d. Choose the option where the usage of the word is incorrect.
BRUSH
- She had a brush with death when she drove off the highway
- You cannot afford to brush aside her ideas
- Peter has to brush his Russian before leaving the country
- You can brush away the dirt from the dress
Answer: (c) Peter has to brush his Russian before leaving the country
Solution: The word brush is followed by ‘up’. The phrasal verb ‘brush up’ is used in the sense of ‘polish up’ or ‘work on’ something
Q. (3) Select the correct alternative.
Olive Ridley Turtles nest only at their birthplace on the coast of Orissa. After a hatchling is born on the beach, it enters the water, migrates to other coasts that are tropical in nature and returns to the coast of its birth to nest only after 15 years or so. Some zoologists have come up with a theory that the turtle recalls the smell of its birth environment and returns to this smell to nest.
Which one of the following if true would undermine the theory of these zoologists?
- Olive Ridleys have a well-developed sense of smell
- Olive Ridleys, when studied in captivity, were found to display a particular preference for pens that contained sand from the Orissa coast.
- Electronic tags attached to Olive Ridleys did not indicate an alteration in their nesting patterns
- Widespread pollution of the world’s oceans is known to have rendered the olfactory systems of marine animals ineffective.
Answer: (d) Widespread pollution of the world’s oceans is known to have rendered the olfactory systems of marine animals ineffective
Solution: Choice (d) makes it clear that turtles have lost their sense of smell due to pollution, thus hampering their ability to return to their nesting grounds.
Q. (4) There are two gaps in the sentence/paragraph given below. Choose from the pair of words given below that will fill the gaps most aptly.
In the post-modern world where ‘borrowings’ are acceptable and the concept of ‘global-local’ is common, the suggestion that contemporary Indian sculptors should consider western influence a/an_______ and looking solely to the indigenous tradition may seem______
- boon, heartening
- embarrassment, pride
- anathema, risible
- bugbear, paradoxical
Answer: (d) bugbear, paradoxical
Q. (5) In the following question, the word given in capital letters is used in four different ways numbered 1 to 4. Choose the option where the usage of the word is incorrect.
PULL
- Pull aside the curtains and let in some air
- I decided to pull away from the coalition due to a difference of opinion with the political partners.
- With his charisma, he can pull the crowd towards his goal.
- The municipal corporation has decided to pull down all illegal tenements in the city.
Answer: (b) I decided to pull away from the frontlines due to a difference of opinion with the political partners.
Solution: Choice (b) is erroneous as ‘pull away’ is an incorrect expression in this context. The correction is ‘….pull out of’ or from’. To pull out of something is to move away from something or stop being involved in it.
Q. (6) There are two gaps in the sentence/paragraph given below. Choose from the pair of words given below that will fill the gaps most aptly.
Evidence from several countries indicates. that_______ pictorial warnings alongside printed text can make even the most ardent tobacco smokers to quit the self-destructive habit and can_____ new users.
- Grotesque, convince
- Innovative, inveigle
- Graphic, exhort
- Emotive, deter
Answer: (d) Emotive, deter
Directions Q. (7-8): Find the synonyms of the words given below in each questions.
Q. (7) Paradigm
- Category
- Difficulty
- Hypothesis
- Foundation
- Proteotype
Answer: e
Q. (8) Distinct
- Infrequent
- Abundant
- Complex
- Cautious
- None of the above
Answer: d
Q. (9) There are two gaps in the sentence/paragraph given below. Choose from the pair of words given below that will fill the gaps most aptly.
The media carries out a social duty cast upon it in a/an________ where governments________ censor or distort shocking occurrences.
- ambience, flourish
- milieu, organisations
- aura, will
- society, exist
Answer: (a) ambience, flourish
Directions Q. (10-13): Seven persons namely A, B, C, D, E, F and G like seven different colours namely, Black, Blue, Red, Yellow, Pink, White and Grey. Each of them works in either of the three companies namely HP, Dell and TCS.
C works in Dell with the one who likes Red. F does not works with C. A works in TCS with only the one who likes Pink. F does not like Black. E works in HP with the one who likes Black. E does not like Grey. The one who likes Grey works with the one who likes Blue but not with C. D works with the one who likes White. D does not like Red. B does not like Black.
Q. (10) Which of the following combinations represents the persons working in Dell?
- D, C
- B, G, C
- F, E, C
- C, B
- E, C, A
Answer: d
Q. (11) Which of the following colours does A like?
- Red
- Grey
- White
- Blue
- Yellow
Answer: c
Q. (12) Which of the following combinations represents the company in which G works and the colours it likes?
- HP – Black
- HP – Red
- Dell – White
- TCS – Blue
- TCS – Yellow
Answer: a
Q. (13) Which of the following combinations is correct?
- D – Grey
- B – Yellow
- C – Black
- F – Pink
- T- Blue
Answer: e
Solutions Q. (10-13):
Person | Company | Colour |
A | TCS | White |
B | Dell | Red |
C | Dell | Yellow |
D | TCS | Pink |
E | HP | Blue |
F | HP | Grey |
G | HP | Black |
Directions Q. (14-15): Read each of the following statements carefully to answer the following questions.
Q. (14) Which of the following expressions will be true if the given expression ‘P > Q ≥ R < S < T’ is definitely true?
- P ≥ Q
- T > R
- S ≥ Q
- P ≥ S
- None of the above
Answer: b
Solution: From the given statement, P > Q ≥ R < S < T, we can derive the following conclusions:
- P > R
- T > R
Q. (15) Which of the following expressions will be true if the given expression ‘P < Q ≤ R > S > T’ is definitely true?
- P < R
- P ≤ R
- S ≤ Q
- P = T
- P < T
Answer: a
Solution: From the given statement, P < Q ≤ R > S > T, we can derive the following conclusions:
- P < R
- T < R
Directions Q. (16-18):
In each question, two equations numbered I and II are given. Solve the equations to determine the relationship betweena and b. Mark the answer as:
- If a < b
- If a > b
- If a ≥ b
- If a ≤ b
- If a = b
Q. (16) I. 4a^{2} + 32a – 36 = 0
II. 5b^{2} – 18b + 16 = 0
Answer: a (a < b)
Solution: Statement I ⇒ 4a^{2} + 36a – 4a – 36 = 0
⇐ 4a (a + 9) -4 (a + 9) = 0
⇐ (4a – 4) (a +9) = 0
⇐ a = -9, 1
Statement II ⇒ 5b^{2} – 10b – 8b + 16 = 0
⇐ 5b (b – 2) -8 (b – 2) = 0
⇐ (5b – 8) (b – 2) = 0
⇐ b = 8/5, 2
Therefore, a < b
Q. (17) I. 14a^{2} + 51a + 7 = 0
II. b^{2} + 2b – 63 = 0
Answer: a (a < b)
Solution: Statement I ⇒ 14a^{2} + 49a + 2a + 7 = 0
⇐ 7a (2a + 7) + (2a + 7) = 0
⇐ (7a + 1) (2a + 7) = 0
⇐ a = -1/7, -7/2
Statement II ⇒ b^{2} + 9b – 7b – 63 = 0
⇐ b(b + 9) – 7(b + 9) = 0
⇐ (b + 9) (b – 7) = 0
⇐ b = -9, 7
Therefore, a < b
Q. (18) I. a^{3 }= -2197
II. b^{2} + 26b + 169 = 0
Answer: e (a = b)
Solution: Statement I ⇒ a = -13
Statement II ⇒ b^{2} + 13 x 2 x b + 13^{2} = 0
⇐ (b +13)^{2} = 0
⇐ b = -13
Therefore, a = b
Q. (19) A bag contains 2 white, 6 black and 7 green marbles. Four marbles are drawn out randomly. Find the probability that none of the marbles drawn is green.
- 19 / 7
- 39 / 2
- 35 / 9
- 25 / 3
- 12 / 7
Answer: b
Solution: Total number of cases = ^{15}C_{4} = (15 x 14 x 13 x 12) / (4 x 3 x 2 x 1)
= 1365
Number of favourable cases = ^{8}C_{4} = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1)
= 70
Therefore, required probability = ^{8}C_{4} / ^{15}C_{4} = 1365 / 70 = 39 / 2
Q. (20) The rate of interest on a sum of money is 4% per annum for the first 5 years, 5% per annum for next 1 year and 8% per annum for the last 2 years. If the simple interest on the sum for a total period of 8 years is Rs. 400, then the sum is
- 900
- 875
- 975.6
- 950
- 1075
Answer: c
Solution: Let, the principle be Rs. y
According to the question,
[{y (4 x 5)} / 100] + [{y (5 x 1)} / 100] + [{y (8 x 2)} / 100] = 400⇐ (20y / 100) + (5y / 100) + (16y / 100) = 400
⇐ 41y / 100 = 400
⇐ y = (400 / 41) x 100
⇐ y = Rs. 975.6
Q. (21) A certain amount of money is divided between Ayushi, Sandhya and Shweta in the ratio 6: 9 : 13. If the difference between the shares of Sandhya and Shweta is Rs. 9800, what will be the difference between the shares of Ayushi and Sandhya?
- Rs. 7500
- Rs. 7350
- Rs. 5000
- Rs. 5700
- Rs. 6500
Answer: b
Solution: Let the shares of Ayushi, Sandhya and Shweta be 6x, 9x and 13x respectively.
According to the question, 13x – 9x = 9800
⇐ 4x = 9800
⇐ x = 9800 / 4
⇐ x = 2450
Therefore, the difference in the shares of Ayushi and Sandhya = 9x – 6x
= (9 X 2450) – (6 X 2450)
= Rs. 7350
Directions Q. (22-23): Study the following information and answer the given questions.
A is the sister of P. P is married to D. D is the father of R. M is the son of H. P is the mother-in-law of H. Q has only one son and no daughter. A is married to L. N is the daughter of L.
Q. (22) How is N related to P?
- Niece
- Sister
- Daughter
- Mother
- Cannot be determined
Answer: a
Solution:
Q. (23) How is A related to R?
- Sister
- Aunt
- Mother-in-law
- Mother
- Cannot be determined
Answer: b
Solution: Since P is the mother of R and A is the sister of P. Therefore, A is the aunt of R.
Directions Q. (24-25): Eight friends A, B, C, D, E, F, G and H are seated in a straight line, facing north, but not necessarily in the same order. G sits at the extreme right end of the line. Only four persons sit between H and C. Both B and F are immediate neighbours of C. Only two people sit between F and E. E is not an immediate neighbour of H. G sits second to the left of A.
Q. (24) What is the position of E with respect to C?
- Third to the right
- To the immediate left
- Second to the right
- Fourth to the right
- Second to the left
Answer: e (E is second to the left of C)
Q. (25) Who amongst the following people represents the person seated at the extreme left end of the line?
- A
- G
- E
- B
- D
Answer: c (E sits to the extreme left end of the line)
Solution Q. (24-25):
Q1. Max bought 20 dining tables for Rs 12,000/- and sold them at a profit equal to the selling price of 4 dining tables. The selling price of 1 dining table is
- 230
- 1200
- 750
- 1000
Answer: C
Solution 1:
Selling Price of 20 dining tables – Cost Price of 20 dining tables = Selling Price of 4 dining
Tables.
S.P. of 16 dining tables = C.P of 20 dining tables. = Rs 12000
S.P. of 1 dining table = 12000/16 = Rs 750/-
Q2. The ages of Charlie and Tango are in the ratio of 5:2 respectively. After 7 years, the ratio of their ages will be 4:3. What is the age of Charlie?
- 5
- 10
- 7
- 8
Answer: A
Solution 2:
Let the present ages of Charlie and Tango be 5x and 2x years respectively.
Charlie’s age 7 years hence = 5x + 7 years
Tango’s age 7 years hence = 2x + 7 years
5x + 7 / 2x + 7 = 4 / 3
15x + 21 = 8x + 28
7x = 7
X = 1
Hence Charlie’s age = 5 years
Q3. 2 pipes can fill a tank in 12 hours and 16 hours respectively. A third pipe can empty the tank in 30 hours. If all 3 pipes are opened and function simultaneously, how much time will the tank take to be full?
- 9.55
- 8.89
- 3.5
- 4
Answer: B
Solution 3:
1st pipe can fill a tank in 12 hours.
Hence the work done in 1 hour = 1/12 = 8.33%
2nd pipe can fill a tank in 16 hours.
Hence the work done in 1 hour = 1/16 = 6.25%
3rd pipe can empty the tank in 30 hours
Hence the negative work done = 1/30 = 3.33%
Therefore total work done in 1 hour
= 8.33 % + 6.25 % – 3.33 %
= 11.25 %
Hence the time taken to fill the tank
= 100 / 11.25
= 8.89 hrs
Q4. Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next 6 years and 12% per annum for the period beyond 10 years. If he pays a total of Rs 12160/- as interest-only at the end of 15 years, how much money did he borrow?
- 8000
- 12000
- 4000
- 7000
Answer: A
Solution 4:
Let the sum of money be Rs a. Then
(a ✕ 8 ✕ 4) / 100 + (a ✕ 10 ✕ 6) / 100 + (a ✕ 12 ✕ 5) / 100 = 12160
32 a + 60 a + 60 a = 1216000
152 a = 1216000
Hence a = Rs 8000/-
Q5. How many metres of carpet 63 cm wide will be required to cover the floor of a room 14 m by 9 m?
- 300
- 900
- 1200
- 200
Answer: D
Solution 5:
Area of floor = 14 ✕ 9
= 126 m^{2}
Length of carpet = ( 126 / 63 ) ✕ 100
= 200 m.
Q6. An artist has completed one-fourth of a rectangular oil painting. When he will paint another 100 square centimetres of the painting, he would complete three-quarters of the painting. If the height of the oil painting is 10 cm, determine the length (in cm) of the oil painting.
- 20
- 40
- 60
- 80
Answer: A
Solution 6:
When the painter completes the painting from half to three quarters he does 100 sQcm of the painting.
Let the total area of the painting be ‘x’
Hence from the above sentence, we can get the expression,
3/4x – 1/4x = 100 cm^{2}
½ x = 100
Therefore, x = 200 cm^{2}
Height is 10 cm, hence
10 ✕ length = 200
Therefore, Length = 20 cm
Q7. A large field of 700 hectares is divided into 2 parts. The difference between the areas of 2 parts is one-fifth of the average of the 2 areas. What is the area of the smaller part in hectares?
- 320
- 490
- 315
- 400
Answer: C
Solution 7:
Let the larger area be ‘a’ hectares.
Let the smaller area be ‘b’ hectares.
As per the details, a + b = 700
And, a – b = {(a + b) / 2} ✕ (⅕)
Solving the above equation we get, a – b = 70
Solving the equations on a + b and a – b
We get; a = 385, b = 315
Q8. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sQft, how many feet of fencing will be required?
- 95
- 88
- 70
- 60
Answer: B
Solution 8:
If one side is 20 ft and the area is 680 sQft, then we can find the breadth of the field.
L ✕ B = 680
L ✕ 20 = 680
L = 34 feet.
Since one of the sides is left open, we need to fence the remaining 3 sides.
The total fencing required is
34 + 20 + 34 = 88 feet.
Therefore, 88 feet of fencing will be required.
Q9. A bag contains 4 red balls, 6 blue balls, and 8 pink balls. One ball is drawn at random and replaced with 3 pink balls. A probability that the first ball drawn was either red or blue in colour and the second ball drawn was pink in colour?
- 11 / 36
- 15 / 44
- 12 / 35
- 11 / 37
Answer: A
Solution 9:
From 4 red and 6 blue balls, we get to choose 1 ball out of 10 balls.
The above logic can be represented as ^{10}C_{1}
The total number of balls are 18. We choose 1 out of them. This can be represented as ^{18}C_{1}
Hence the probability of the first event of withdrawing 1 red or blue ball is
= ^{10}C_{1 }/ ^{18}C_{1}
In the second event 1, red/blue ball is replaced with 3 pink balls. In total there is the addition of 2 balls to the total number of balls previously available.
Hence the total number of balls is 20 and the total number of pink balls is 8 + 3 = 11
Hence the probability of withdrawing 1 pink ball
= ^{11}C_{1} / ^{20} C_{ 1}
Hence to find the probability that the first ball drawn was either red or blue in colour and the second ball drawn was pink in colour is given by
= (^{10}C_{1 }/ ^{18}C_{1}) ✕ ( ^{11}C_{1} / ^{20} C_{ 1} )
= 11 / 36
Directions (10 – 14): Rearrange the following sentences to form a meaningful paragraph.
- That the intention was to target India is apparent in the selection of both the panellists and the topics. Two of those who testified are well known for their tirades against India for decades. The panellists from Pakistan was low-key, to say the least since any real testimony would have knocked Pakistan out of the court entirely.
- Sweets are the uses of adversity, says an exiled Duke in Shakespeares As You Like It, going on to ponder on lessons to be found in running brooks and sermons in stones, and such like. Following the hearing on Human Rights in South Asia in the House Sub Committee – that was frankly disastrous for India, it may be useful to adopt this attitude and look for those lessons, even if that’s not an exercise we generally adopt.
- Anyone who watched the hearing by the House Foreign affairs Subcommittee on Asia and the Pacific would have discerned not only that India got a drubbing and that Pakistan got away scot-free but also that the State Department gave a far more professionally-measured statement than the panellists themselves.
- Assistant Secretary of State for South and Central Asia Alice Wells statement praised India as a US partner, ticked all the right boxes, including terrorist intimidation, and called out Pakistan’s continued support to terrorists groups” as the main obstacle. Wells presented facts which was more than could be said of the rest. One of those present and testifying had previously been fired from for the California Institute of Integral Studies for the ‘reckless violation’ of professional ethics.
- Another one, whose novel was exhausting to read, continued to rely on fiction citing ‘Government sources’ which were anything but. Yet another, otherwise articulate panellist, relied almost entirely on the standard Indian handouts. If that narrative had worked, there would have been no need for hearing in the first place.
Q10. Which of the following is the first sentence?
- 2
- 4
- 5
- 1
Answer: A
Q11. Which of the following is the second sentence?
- 2
- 3
- 1
- 5
Answer: B
Q12. Which of the following is the third sentence?
- 5
- 2
- 4
- 3
Answer: C
Q13. Which of the following is the fourth sentence?
- 1
- 3
- 4
- 5
Answer: D
Q14. Which of the following is the last sentence?
- 1
- 2
- 4
- 5
Answer: A
Directions (15 -19): Fill in the blanks with the right word.
Q15. That month, the US unemployment rate dropped below 6 %, and a broad range of commentators assured us that inflation would soon be on the rise, as predicted by the Phillips curve. The ———- of this argument, of course, was that the US Federal Reserve should begin rapidly normalizing monetary policy.
- Insinuation
- Indictment
- Incrimination
- Corollary
Answer: D
Q16. To be sure, the —————-wisdom among economists back in the 1990’s was justified. Between 1957 and 1988, inflation responded predictably to fluctuations in the rate of unemployment.
- Atypical
- Spurned
- Conventional
- Fluctuating
Answer: C
Q17. And as these jobs disappear, so, too, will social contacts between socio-economic classes, and between immigrants and natives. The broader question, then, is the impact of the ———– loss of involuntary social mixing on diverse, multi-ethnic societies.
- Bygone
- Impending
- Deferred
- Delayed
Answer: B
Q18. But as citizens of ———– democracies, we should recognise what is at stake when we use technology to disintermediate economic interactions. There may come a time when we need to subsidize expensive, less “efficient” work, much as we do now with renewable energy.
- Identical
- resembling
- Diverse
- Conforming
Answer: C
Q19. Trump’s withdrawal from TPP is the canonical example of his trade policy recklessness. Signed in 2016 by the United States and 11 other Pacific Rim countries, the treaty would have governed around 40% of all trade covered by World Trade Organisation Rules.
- Unprecedented
- Canonical
- Pioneering
- Experimental
Answer: B
Directions (20 – 25): Answer the questions on the basis of codes given below.
‘Il be pee’ means ‘roses are blue’, ‘sik hee’ means ‘red flowers’ and ‘pee mit hee’ means ‘flowers are vegetables.’
Q20. How is ‘red’ written in that code?
- Sik
- Hee
- Mit
- Pee
Answer: A
Solution 20:
From the statements sik hee – red flowers and pee mit hee – flowers are vegetables we can see that code hee is common in both sentences, and flowers are common word in both deductions. Hence hee stands for flowers.
From the sentences il bee pee and pee mit hee we can see pee is common and are is common. Hence pee stands for are.
In sik hee means red flowers, we know hee stands for flowers, hence sik stands for red. In pee mit hee, we have deduced the meaning of mit and pee, the remaining code is pee, hence pee stands for vegetables.
From the above deduction, we can see that sik stands for red.
Q21. How is ‘roses’ written in that code?
- Mit
- Pee
- Cannot be determined
- None of these
Answer: C
Solution 21:
From the logic provided earlier, we can see that the meaning of roses cannot be determined.
Q22. How is ‘vegetables are red flowers’ written in this code?
- Mit pee sik hee
- Il Mit sik pee
- Il hee be
- Be Mit Sik hee
Answer: A
Solution 22:
From the logic shared earlier, we can codify ‘vegetables are red flowers’ as ‘mit pee sik hee’
Directions (23 – 25): Answer the questions as per the given code
In a certain code language ‘481’ means ‘sky is blue’, ‘246’ means ‘sea is deep’ and ‘698’ means ‘sea looks blue.’
Q23. What number is the code for deep?
- 2
- 1
- 6
- 4
Answer: A
Solution 23: 2
From the given statements we can come to the following conclusions about the codes.
From 481 – sky is blue and 246 – sea is deep
Common word – ‘is’ and common digit – 4. Hence ‘is’ stands for ‘4’.
481 – sky is blue, 698 – sea looks blue.
Common word – ‘blue’ and common digit – ‘8’. Hence blue stands for 8.
In 481- sky is blue, remaining digit – 1 and remaining word – sky. Hence ‘sky’ is ‘1’
246 – sea is deep and 698 – sea looks blue; common digit – 6, common word – sea.
Hence ‘sea’ is coded as 6.
In 246 – sea is deep; remaining word – deep and remaining digit – 2
Hence ‘deep’ stands for ‘2’
698 – sea looks blue, remaining word – looks, remaining digit – 9
Hence looks stands for 9.
Blue – 8
Sea – 6
Is – 4
Deep – 2
Sky – 1
Looks – 9
Q24. What number stands for code ‘blue’?
- 6
- 1
- 9
- 8
Answer: D
Solution 24: 8
From the above conclusions, we can say blue is 8.
Q25. What number is the code for ‘sea’?
- 8
- 4
- 6
- 9
Answer: C
Solution 25: 6
Q 1. A person counted in the following way on the fingers of the left hand. Started numbering thumb as 1, the index finger as 2, middle finger 3, ring finger 4, little finger 5, then reversed direction, calling the ring finger 6, middle finger 7, index finger 8, thumb 9, and then back to the index finger for 10, middle finger for 11, and so on. The person counted up to 1994 and on which finger did the person end up?
- Index
- Ring
- Thumb
- Little
Answer: A
Solution 1:
We can see that thumb is numbered in the following sequence,
1, 9, 17, 25, ……
We can notice that the numbers are in Arithmetic Progression,
First-term a = 1, common difference d = 9 – 1 = 8
The nth term will be
T_{n} = a + (n – 1) d
= 1 + (n – 1)8
= 8n – 7
8n – 7 = 1994
n = (1994 + 7) / 8
Hence, n = 250
T_{250} = 1 + (250 – 1) 8
= 1993
Hence 1993 is the thumb, and 1994 is the index finger.
Q 2. 7 is added to a certain number; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. Thus if the remainder left is 12, what was the original number?
- 12
- 20
- 30
- 65
Answer: B
Solution 2:
Let the original number be ‘a’
From the first 3 sentences, we can get the expression, [ (a + 7) 5 ] / 9
From the remaining sentences, we can get the expression,
[ { (a + 7) 5 } / 9 ] – 3 = 12Hence, a = 20
Q 3. If x + y = 17, and xy = 76, then what is the value of x^{2} + y^{2} ?
- 197
- 186
- 134
- 137
Answer: D
Solution 3:
(x + y)^{2} = x ^{2} + y^{2 } + 2xy
X^{2} + y^{2} = (x + y)^{2} – 2xy
= (17)^{2} – 2 (76)
= 137
Q 4. What is the number of prime factors contained in the product
33^{7} ✕ 21^{8} ✕ 18^{10} ✕ 6^{6}
- 34
- 87
- 15
- 72
Answer: D
Solution 4:
33^{7} = (11 ✕ 3)^{7}
21^{8} = (7 ✕ 3)^{8}
18^{10} = (3^{2} ✕ 2)^{10}
6^{6} = (3 ✕ 2)^{6}
33^{7} ✕ 21^{8} ✕ 18^{10} ✕ 6^{6} can be rewritten as
11^{7} ✕ 3^{7} ✕ 7^{8} ✕ 3^{8} ✕ 3^{20} ✕ 2^{10} ✕ 3^{6} ✕ 2^{6}
2^{(10+6)} ✕ 3^{(7+8+20+6)} ✕ 7^{8} ✕ 11^{7}
2^{16 }✕ 3^{ 41} ✕ 7^{8} ✕ 11^{7}
Therefore the number of prime factors
= 16 + 41 + 8 + 7
= 72
Q 5. The least number of square tiles required to pave the floor of a room 15 m 17 cm long and
9 m 2 cm broad is
- 814
- 231
- 155
- 189
Answer: D
Solution 5:
For easier calculation, it is better to convert the measurements to the same unit.
15 m 17 cm = 1500 m + 17 cm = 1517 cm
9 m 2 cm = 900 cm + 2 cm = 902 cm
HCF of 1517 cm and 902 cm is 41 cm
Required number of tiles = Area of floor / Area of each tile
= (1517 ✕ 902) / (41 ✕ 41)
= 814
Q 6. A crate of mangoes contains 1 bruised mango for every 30 mangoes in the crate. If 3 out of every 4 bruised mangoes are considered unsaleable, and there are 12 unsaleable mangoes in the crate, then how many mangoes are in the crate.
- 200
- 480
- 100
- 250
Answer: B
Solution 6:
Let the total number of mangoes in the crate be x. Then,
Number of bruised mangoes = (1 / 30) x
Number of unsaleable mangoes = ( ¾ ✕ 1/30 x) = 1/40 x
(1/40) x = 12
Hence, x = 480 mangoes
Q 7. There are some lions and some hornbills in the forest. If the total number of animal heads in the forest is 1058 and the total number of animal legs is 3046, what is the number of hornbills in the forest?
- 593
- 230
- 130
- 250
Answer: A
Solution 7:
Let the total number of hornbills in the forest be ‘x’
Let the total number of lions in the forest be ‘y’
The total number of heads is 1058, it indirectly implies that 1058 is the total number of lions and hornbills
X + y = 1058 —— (1)
The total number of legs = 3046.
Hornbills have 2 legs so we can consider it as 2x.
Lions have 4 legs so we can consider it as 4y
Therefore, 2x + 4y = 3046 ——- (2)
Solving equation 1 and 2
Y = 465
Substituting the value of y in equation 1, we get
X = 1058 – 465
X = 593
Therefore the number of Hornbills = 593
Q 8. The average age of husband and wife was 26 years at the time of marriage. After 5 years they have a one-year-old child. The average age of the family now is.
- 23
- 21
- 15
- 19
Answer: B
Solution 8:
Sum of the present ages of the family
= (26 ✕ 2) + (5 ✕ 2) + 1
To get the total we multiply the average age of people with the number of people. 26 was the average age and the number of people was 2, after 5 years we multiply 5 with the number of people i.e. 2.
= 52 + 10 + 1
= 63 years.
The average age of the family = 63 / 3 = 21 years.
Q 9. The falling height of an object is proportional to the square of the time. One object falls
120 cm in 4 seconds, then in 10 seconds from what height will the object fall?
- 650
- 250
- 124
- 750
Answer: D
Solution 9:
The height from which the object falls is directly proportional to the time.
Let us consider height as ‘h’ and time as ‘t’
Let h_{1} = 120 cm, t_{1} = 4 seconds. t_{2} = 10 seconds. We need to find h_{2}
As per proportionality, h_{1} / h_{2} = t_{1}^{2} / t_{2}^{2}
120 / h_{2} = 4^{2} / 10^{2}
Hence, h_{2} = (120 ✕ 100) / 16
h_{2 } = 750 cm
Hence the required height = 750 cm.
Q 10. If each of the twelve digits on a clock is substituted by English vowels a, e, i, o, u in sequence 1 by ‘a’, 2 by ‘e’, 3 by ‘i’, 4 by ‘o’, 5 by ‘u’ the hour and minute hand will be between pair of which vowels at 2:25 PM.
- i,o
- a,e
- u,o
- a,o
Answer: A
Solution 10:
At 2:30 the hour hand will be at 2 and the minute hand will be at 5.
2 is replaced with ‘e’ and 5 is replaced with ‘u’
The numbers in between are 3 and 4. 3 is replaced with ‘i’ and 4 is replaced with ‘o’
Hence the vowels are ‘i’ and ‘o’
Q 11. If Y = 25, MERCK = 50, then what is the value of NED?
- 33
- 14
- 23
- 53
Answer: C
Solution 11:
The alphabets have been numbered as per their position in the English alphabets.
MERCK
= 13 + 5 + 18 + 3 + 11
= 50
Similarly NED
N = 14, E = 5, D = 4
NED
= 14 + 5 + 4
= 23
Directions (12 – 16): Study the following information arrangement carefully and answer the questions given below.
W 1 R % 4 J E # 7 M T 2 I 9 B H 3 A $ 9 F Q 5 D G 6 U S P
Q 12. Which of the following is the seventh to the right of the eighteenth from the right end?
- $
- #
- 9
- P
Answer: A
Solution 12:
2 is 18th from the right end.
$ is seventh to the right of 2.
Q 13. If the order of the last fifteen elements is reversed, which of the following will be fifth to the right of twelfth from the left end?
- U
- P
- A
- $
Answer: A
Solution 13:
When the order of the last fifteen elements is reversed the following order will be formed
P S U 6 G D 5 Q F 9 $ A 3 H B
Twelfth from the left end will be 2.
Fifth to the right of 2 is U.
Q 14. Four of the following 5 are alike in a certain way on the basis of the above arrangement and hence form a group. Which one does not belong to that group?
- 3B$
- 7ET
- 5FG
- 9QA
Answer: D
Solution 14:
From the sequence, we can find that 4 is the answer. In all the other 3 options, 2nd letter is -2 to the digit in the first position, and the 3rd symbol or letter is +2 from the digit in the 1st position.
Q 15. If the positions of E and A are interchanged and similarly the positions of R and U are interchanged then how many symbols will be there each of which is either preceded or followed by a vowel?
- 2
- 3
- 1
- 4
Answer: B
Solution 15:
The answer is 3 symbols.
% is preceded by U.
# is preceded by A.
$ is preceded by E.
Q 16. What should come in place of the question mark on the basis of the above arrangement?
R 4 # M 2 B 3 $ Q ?
- M9B
- WQ5
- D6P
- QDG
Answer: C
Solution 16:
There are 3 groups here.
In the 1st group, 2nd element 4 is 2 positions away from first element R and 3rd element # is 3 positions away from the 2nd element 4.
In the 2nd group, the 2nd element 2 is 2 positions away from the first element M and 3rd element B is 3 positions away from the 2nd element 2.
In the 3rd group, the 2nd element $ is 2 positions away from the first element 3 and the 3rd element Q is 3 positions away from the 2nd element $.
Another important point to notice is that there is a difference of 7 positions between 1st term of group 1 and group 2; difference of 7 positions between 1st term of group 2 and group 3.
Hence the 1st term of the succeeding group will be a difference of 7 positions from 3 i.e. D.
The 2nd element will be 2 positions away from D; i.e. 6 and 3rd element will be 3 positions away i.e. P.
Hence the terms in the new group will be D6P
Directions (17-21): Rearrange the given 5 sentences in a proper sequence so as to form a meaningful paragraph.
- It is significant to note that of the two projects approved by DAC under Make-II, DRDO is already engaged in the development of ATGM. The R&D agency seems to have achieved a degree of success in the project. This is the reason why the Government has twice ignored in the past an import option in favour of the home grown project.
- In a major boost to Make in India and private sectors participation in defence production, in particular, the Defence Acquisition Council (DAC) on October 21 approved three capital procurement projects worth Rs 3300 crore for indigenous design and development. The first 2 projects pertain to Make – II category of the Defence Procurement Procedure (DPP) and include third-generation anti-tank guided missiles (ATGM) and auxiliary power units for T-72 and T-90 tanks.
- The third project relates to the design and development of the (D&D) of the Electronic Warfare (EW) systems for mountain and high altitude terrain by the Defence Research and Development Organisation and manufacturing of the same by design-cum-production partner selected from the industry.
- The importance of DAC’s October 21 decision is that it is the first time that the Government has allowed the private sector to undertake D&D of complex defence equipment, a task which was hitherto reserved for the DRDO and, to a smaller extent, state-owned/controlled production entities.
- The Government’s bold decision to allow the private sector to undertake complex D&D is a step in the right direction to forge a larger innovation system to meet the diverse requirements of national security. However, caution may be required to avoid duplication of efforts and prevent indirect import which is otherwise not permitted directly.
Q 17. Which of the following is the first sentence?
- 5
- 3
- 2
- 1
Answer: C
Q 18. Which of the following is the last sentence?
- 4
- 1
- 2
- 5
Answer: B
Q 19. Which of the following is the 2nd sentence?
- 3
- 2
- 1
- 5
Answer: A
Q 20. Which of the following is the 3rd sentence?
- 3
- 2
- 1
- 4
Answer: D
Q 21. Which of the following is the fourth sentence?
- 4
- 5
- 1
- 2
Answer: B
Directions (22 – 25): Fill in the blanks with the appropriate word.
Q 22. Others claim that Chileans are simply fed up with the ——— of markets and profit seeking into every corner of daily life.
- Recession
- Retraction
- Submission
- Intrusion
Answer: D
Q 23. Again this hypothesis has an air of ———-. Polls show widespread dissatisfaction with private companies that provide public services ranging from water and electricity to health insurance and pension-fund administration.
- Plausibility
- Incongruousness
- Dubiety
- Unlikeliness
Answer: A
Q 24. And in 2017 a substantial ———– of Chileans voted for President Sebastian Pinera, a billionaire businessman and unabashed apologist for capitalism who ran on a platform of reigniting growth.
- Smidgeon
- Pittance
- Dram
- Plurality
Answer: D
Q 25. Regulatory regimes designed to ensure investment in utilities, for example, have given companies excessive ——— to keep prices high. Likewise, Chile’s pharmacy chains have been found guilty of collusion and price gouging, as have chicken farmers and long haul bus companies.
- Embargo
- Tautness
- Rigidity
- Leeway
Answer: D
Q 1. Of the three numbers, the sum of the first two is 73; the sum of the second and the third is 77 and the sum of the third and thrice the first is 104. The third number is
- 29
- 90
- 13
- 65
Answer: A
Solution 1:
Let the 3 numbers be a, b, c.
As per details in the question, a + b = 73
and , b + c = 77
So, b = 77 – c
Substitute value of b in a + b = 73
We get, a + 77 – c = 73
Hence, a = c – 4
C + 3 a = 104
Substituting the value of ‘a’ in the above equation,
So, c + 3(c – 4) = 104
4c = 104 – 12
4c = 116
C = 29
Hence the value of the third number is 29.
Q 2. In a mathematics examination, the numbers scored by 4 candidates are 4 successive odd integers. If their total marks are 185, the highest score is
- 54
- 49
- 80
- 15
Answer: B
Solution 2:
To make the right assumptions on the unknown numbers candidates must always remember the following rules for faster calculations.
Odd number + odd number = Even number
Even number + even number = Even number
Odd number + Even number = Odd number
Even number + Odd number = Odd number
Let the numbers be x , x + 2, x + 4, x + 6
Over here let x be the odd number. Hence when the odd number is added to an even number the resultant number will be an odd number. Hence we have 4 consecutive odd numbers represented above. If we had used x + 1, x + 3, x + 5, then we would have ended with consecutive even numbers, since we had to assume x as an odd number, and odd number added to odd number would have resulted in an even number.
X + X + 2 + X + 4 + X + 6 = 185
4x = 185 – 13
4x = 172
X = 43
Hence the highest score is 43 + 6 = 49
Q 3. A can do a piece of work in 10 days; B in 15 days. They work for 5 days. The rest of the work was finished by C in 2 days. If they get Rs 1500/- for the whole work, the daily wages of B and C are
- 540
- 200
- 225
- 548
Answer: C
Solution 3:
This problem will be lengthy if done through the method of fractions.
But if we internalise the fractions to percentage conversion method this can be done very quickly.
A can do a piece of work in 10 days
1/10 = 10 %
Therefore A can do 10 % of the work in 1 day.
B can do a piece of work in 15 days
1/15 = 6.66 %
Therefore B can do 6.66 % of the work in 1 day.
Total work done by A in 5 days = 10 * 5 = 50 %
Total work done by B in 5 days = 6.66 * 5 = 33.33 %
Hence, total work done by A and B in 5 days = 83.33 %
C does 100 – 83.33 = 16.67 % work in 2 days.
1 day work done by C = 16.67 / 2 = 8.33 %
Therefore daily wage of B
= (6.66 / 100 ) * 1500
= Approx Rs 100
Daily wage of C = (8.33 / 100 ) * 1500
= Approx Rs 125
Hence the daily wages of B and C = 100 + 125 = Rs 225/-
Q 4. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same work in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
- 10
- 3
- 15
- 4
Answer: D
Solution 4:
Let 1 man’s 1 day work = x
Let 1 boy’s 1 day work = y
Then, 6x + 8y = 1 /10
26x + 48y = 1 / 2
Solving the 2 equations we get,
X = 1 / 100 and y = 1 / 200
Therefore 1-day work of 15 men and 20 boys
= 15 ( 1/ 100 + 1/ 200 )
= 1 / 4
Therefore 15 men and 20 boys can finish the work in 4 days.
Q 5. Water flows at the rate of 20 metres per minute from a cylindrical pipe of 15 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 60 cm and depth 36 cm?
- 9 minutes 36 seconds
- 10 minutes 55 seconds
- 15 minutes 40 seconds
- 7 minutes 45 seconds
Answer: A
Solution 5:
Water that can be filled in the conical vessel is given by the volume of the conical vessel.
The volume of Cone = ⅓ 𝜋r^{2} h
Radius = 30 cm, height = 36 cm.
= ⅓ ✕ 𝜋 ✕ 30^{2} ✕ 36
= 𝜋 ✕ 30^{2} ✕ 12
The volume of water flown in the cylindrical pipe = 𝜋r^{2} h
= 𝜋 ✕ (7.5 / 10) ✕ (7.5 / 10) ✕ 2000
Hence, [ 𝜋 ✕ 30^{2} ✕ 12 ] / [ 𝜋 ✕ (7.5 / 10) ✕ (7.5 / 10) ✕ 2000 ]
= 9.6 minutes
= 9 minutes 36 seconds.
Q 6. 2 trains pass each other on parallel lines. Each train is 100 metres long. When they are going in the same direction, the faster one takes 60 seconds to pass the other completely. If they are going in opposite directions they pass each other completely in 10 seconds. Find the speed of the slower train in km/hr.
- 15
- 25
- 30
- 35
Answer: C
Solution 6:
Let the speed of the faster train be S_{1}
Let the speed of the slower train be S_{2}
When the 2 trains travels in the same directions the relative speed will be S_{1} – S_{2}
And the distance traveled will be equal to the sum of the lengths of the trains which is equal to 100 + 100 = 200 m
When the 2 trains travels in the opposite directions the relative speed will be S_{1} + S_{2}
And the distance travelled will be equal to the sum of the length of the trains is equal to 200 m.
S_{1} + S_{2 } = Distance / time = 200 / 10
S_{1} + S_{2} = 20
S_{1} – S_{2} = 200 / 60 = 10 / 3
Multiply the above equation by 3.
3S_{1} – 3S_{2} = 10
S_{1} + S_{2} = 20
Solving the above 2 equations we get,
6S_{1} = 70
S_{1} = 70 / 6
S_{2} = 20 – (70 / 6)
S_{2} = ( 50 / 6 ) ✕ (18 / 5)
S_{2} = 30 Kmph
Q 7. Veer runs 100 metres in 20 seconds and Andy runs the same distance in 25 seconds. By what distance will Veer beat Andy in a hundred metre race?
- 20
- 15
- 40
- 50
Answer: A
Solution 7:
Speed of Veer = Distance travelled / time taken = 100 / 20 = 5 m/s
Speed of Andy = Distance travelled / time taken = 100 / 25 = 4 m/s
Veer travels 100 metres in 20 seconds.
Hence the distance travelled by Andy in 20 seconds = Time ✕ Speed
= 20 ✕ 4 = 80 metres.
Hence Veer beats Andy by 20 metres.
Directions (8-9): Find the next number in the series.
Q 8. 4, 12, 39, 105, 230, 446, ?
- 800
- 125
- 789
- 1200
Answer: C
Solution 8:
4 + 2^{3} = 4 + 8 = 12
12 + 3^{3} = 12 + 27 = 39
39 + 4^{3} = 39 + 64 = 104
104 + 5^{3} = 105 + 125 = 230
235 + 6^{3} = 230 + 216 = 446
446 + 7^{3} = 446 + 343 = 789
Q 9. 3, 7, 16, 41, 90, 211, 380, ?
- 800
- 669
- 329
- 457
Answer: B
Solution 9:
3 + 2^{2} = 3 + 4 = 7
7 + 3^{2} = 7 + 9 = 16
16 + 5^{2} = 16 + 25 = 41
41 + 7^{2} = 41 + 49 = 90
90 + 11^{2} = 90 + 121 = 211
211 + 13^{2} = 211 + 169 = 380
380 + 17^{2} = 380 + 289 = 669
Directions (10 – 14): Answer the questions based on the following information.
From time to time, the Managing Director of a company appoints planning committees, each consisting of exactly 3 members. Eligible for appointment are three executives from Finance – B, C and D – and three executives from Operations – E, F and M.
Any given committee is subject to the following restrictions on appointments:
(i) At least 1 member must be Finance, and at least one member must be from Operations.
(ii) If B is appointed, C cannot be appointed.
(iii) Neither D nor F can be appointed unless the other is also appointed.
(iv) If E is appointed, M must be appointed.
Q 10. Which of the following is an acceptable committee?
- E, F and M
- D, E and F
- D, F and M
- B, D and M
Answer: C
Solution 10:
From the given conditions we can find that D, F and M is an acceptable committee.
Q 11. If appointees from Operations are in majority in a committee, that committee must include
- M
- F
- E
- C
Answer: A
Solution 11:
A committee is made up of 3 members, if the majority of them are from Operations, it implies the committee has 2 members of operations. There are different ways of electing 2 members from Operations, it could EM, EF, FM. EF is not a possible combination because as per rule 4, if E is elected then M has to be elected. Hence we can conclude that the committee must include M.
Q 12. If the restrictions on appointments apply also to a four-member committee appointed from the same group of executives, which of the following will be true?
- If B is appointed, M must also be appointed.
- If F is appointed, C must also be appointed.
- If C is appointed, E must also be appointed.
- None of the above will be true.
Answer: A
Solution 12:
From the given conditions we can find that option 1 is the right answer.
Q 13. If B is appointed to the same committee as M, which of the following will be true of that committee?
- E is not a committee member
- F is a committee member
- Appointees from Finance are in the majority
- Appointees from operations are in the majority.
Answer: D
Solution 13:
From the given conditions, we can see that option 4 is the answer. As B is appointed, C cannot be appointed, and if D is appointed then has to be accommodated which will result in having 4 members in the committee. Hence C and D are ruled out and the remaining 1 position will be filled by members of the operation. So there will be 2 members from operations as M is already present in the committee.
Q 14. If appointees from Finance are in majority on a committee, that committee must include
- B
- C
- F
- M
Answer: C
Solution 14:
Clearly, 2 members are from Finance. If B is appointed then C cannot be appointed. Hence if B is appointed then other Finance member has to be D and if D is to be appointed then F has to appointed. If C is appointed then B cannot be appointed hence D has to be the other Finance member, if D is there then by default F has to be there. From both the above combinations we can see that F has to be appointed. Hence 3 is the answer.
Directions (15 – 18): Read the conditions, and answer the questions given below
In an examination, six subjects were available for a candidate of which only three had to be offered under the following conditions:
One who offered A had to offer B also and vice versa. One who offered A could not offer E. One who offered C could not or D could not offer F. The distribution of candidates over the subjects were as follows.
A – 70, B – 70, C – 90, D – 85, E – 70, F – 35
Q 15. How many combinations were permitted?
- 4
- 5
- 6
- 7
Answer: A
Solutions 15:
From the given conditions, we can say that 4 combinations are possible – ABC, ABD, ABF, CDE.
Q 16. How many candidates offered the combinations A + B + C?
- 15
- 20
- 35
- 70
Answer: B
Solution 16:
From the given conditions we can find that the answer is 20.
Q 17. How many candidates combined C with D?
- 15
- 20
- 35
- 70
Answer: D
Solution 17:
From the given conditions we can find that the answer is 70.
Q 18. How many candidates offered B with F?
- 15
- 20
- 35
- 70
Answer: C
Solution 18:
From the given conditions we can find that the answer is 35.
Directions (19-23): Rearrange the given 5 sentences in a proper sequence so as to form a meaningful paragraph.
- Their central insight was mostly intuitive: even subsistence farmers know that improving one’s life in the future requires saving some money in the present, in order to purchase another piece of land or better equipment with which to improve one’s current plot.
- This year’s Nobel Memorial Prize in Economic sciences recognizes Abhijit Banerjee, Esther Duflo, and Michael Kremer for their work using Randomized control trials (RCT’s) in developmental studies. This year’s selection has elicited a broad array of reactions from around the world, not least because RCT’s are a source of controversy among academic economists.
- To many in China, the Nobel committee seems once again to have missed the Chinese Development experience, which after all had nothing to do with RCT’s. To be sure, some of this criticism amounts to sour grapes. The Nobel prize has been awarded to only 3 Chinese nationals – for literature, medicine, and peace – since its inception.
- Nonetheless, China’s economic history offers important lessons that today’s RCT driven approach to development research has missed. Researchers in the field seem to have forgotten the wisdom imparted by the classical development economists of the 1950s: economic development is about taking the difficult but necessary steps to achieve sustained growth.
- For example, increasing domestic savings is very difficult but imperative. Classical development economists such as Pei – Kang Chang, Roy F Harrod, Evsey Domar, and Robert Solow saw that savings are essential for jump-starting economic growth in a poor country.
Q 19. Which of the following is the first sentence?
- 4
- 2
- 5
- 1
Answer: B
Q 20. Which of the following is the second sentence?
- 3
- 1
- 4
- 5
Answer: A
Q 21. Which of the following is the third sentence?
- 2
- 3
- 4
- 1
Answer: C
Q 22. Which of the following is the fifth sentence?
- 1
- 3
- 2
- 4
Answer: D
Q 23. Which of the following is the fourth sentence?
- 5
- 2
- 1
- 4
Answer: A
Directions (24 – 25): Fill in the blanks with the appropriate word.
Q 24. Today, security is indivisible. Events in one region of the world have an impact, both positive and negative, on other regions. This highlights the necessity of combining strengths to ———- new compacts that can appropriately deal with emerging challenges.
- Dismantle
- Wreck
- Demolish
- Forge
Answer: D
Q 25. India believes in ancient Sanskrit saying “Vasudhaiva Kutumbakam”, which means that the entire world is one family. India’s family in South Asia ———–its several neighbours.
- Preclude
- Prohibit
- Reject
- Comprise
Answer: D
Q 1. If a/b = ⅓, b/c = 2, c/d = ½, d/e = 3, e/f = ¼, then what is the value of abc / def ?
- ⅜”,
- 2/9″,
- 3/7″,
- 1/6″,
Answer: 1
Solution 1:
a/b = ⅓
We get, b = 3a
b/c = 2
c= b/2
Substituting the value of b,
c= 3a / 2
Hence, abc = a * 3a * (3a/2)
c/d= ½
d= 2c = 2 (3a / 2) = 3a
d/e= 3
e= d / 3 = 3a / 3 = a
e /f = 1 / 4
f= 4e = 4a
abc/def = [a * 3a * (3a/2)] / [ 3a * a * 4a ]
= 9/2 a^{3} * (1 / 12a^{3}) = ⅜
Q 2. The expression ( 1 + ⅓ ) ( 1 + ¼ ) (1 + ⅕) …….(1+ 1/n)
- 10″,
- (n+1) / 3″,
- N”,
- N + 10″,
Answer: 2
Solution 2:
Given expression can be rewritten as
(4/3) ✕ (5/4) ✕ (6/5) …. ✕ (n+1) / n
In the denominator, 3 remains and in the numerator (n + 1) remains.
= (n+1) / 3
Q 3. At a party, 15 people shake hands with each other. How many times did the handshake take place?
- 120″,
- 148″,
- 105″,
- 129″,
Answer: 3
Solution 3:
The first man shakes hands with 14 other people.
2nd man shakes hands with 13 other people since he has already shaken hands with 1st man.
3rd man shakes hands with 12 other people since he has already shaken hands with 1st and 2nd man.
Hence we get the following series,
14 + 13 + 12 + …..+ 1
= (14 ✕ 15) / 2
= 105
Q 4. What is greater of the 2 numbers whose product is 1092 and the sum of the two numbers exceeds their difference by 42?
- 52″,
- 39″,
- 87″,
- 59″,
Answer: 1
Solution 4:
Let the 2 numbers be ‘x’ and ‘y’
Product of the 2 numbers xy = 1092
Sum of 2 numbers exceeds the difference of the 2 numbers can be given below as,
(x + y) – (x – y) = 42
2y = 42
So, y = 21
Substitute y in xy = 1092
X = 1092 / 21
Hence, x = 52.
The bigger number is 52.
Q 5. The ages of 2 persons differ by 20 years. If 5 years ago, the older one be 5 times as old as the younger one, then their present ages are
- 20″,
- 10″,
- 40″,
- 50″,
Answer: 2
Solution 5:
Let the present ages of both of them be
‘X’ years and ‘x – 20’ years.
5 years ago their ages were
X – 5 = 5 [(x – 20) – 5]
4x = 120
X = 30 years
Age of person younger to him = 30 – 20 = 10 years.
Q 6. Sharath had a Mathematics test which had 175 problems, 95 arithmetic,30 Algebra, 45 Geometry problems. Although he answered 60% of the Arithmetic, 40% of Algebra, 60% of Geometry problems correctly, he did not pass the test because he got less than 80% of the problems right. How many more questions he would have answered correctly to earn the 80% passing grade?
- 23″,
- 15″,
- 44″,
- 16″,
Answer: 3
Solution 6:
Total number of questions = 175
Number of questions to be answered correctly to pass the examination
= 80% of 175
= (4/ 5 ) * 175 = 140 questions
Questions answered correctly section wise.
60% of 95 Arithmetic questions = (3 / 5 ) * 95 = 57
40% of 30 Algebra questions = (⅖ ) * 30 = 12
60% of 45 Geometry questions = ( ⅗ ) * 45 = 27
Total number of questions answered correctly = 57 + 12 + 27 = 96
Hence the additional number of questions that need to be answered correctly
= 140 – 96 = 44
Q 7. A, B and C can separately do work in 12, 15 and 20 days respectively. They started to work together but C left after 2 days. The remaining work will be finished in?
- 10″,
- 3″,
- 7″,
- 4″,
Answer: 4
Solution 7:
The best way to solve this problem is through fraction to percentage conversion method.
A can complete a work in 12 days.
A’s 1-day work = 1/12 = 8.33%
B can complete a work in 15 days.
B’s 1-day work = 1/15 = 6.66%
C can complete a work in 20 days.
C’s 1-day work = 1/20 = 5%
The total work done by all 3 of them in 1 day
= 8.33 + 6.66 + 5
= 20%
All three of them worked together for 2 days
Hence the work completed in 2 days = 40%
Remaining 60% of the work is done by A and B.
Together they can do 15% work in 1 day.
Hence days required to complete 60% of work by both of them
= 60 / 15
= 4 days
Directions (8 – 12): Study the information and answer the questions given below.
Seven boys A, B, C, D, E, F and K live in three different buildings – The Shard, Cayan Tower and One Madison. Each of them flying different colours i.e. red, green, blue, white, black, yellow and pink, not necessarily in that order. Not more than three or less than two stays in any of the buildings. F is flying a pink kite and lives in the same building as only K i.e. The Shard. C is flying a black kite and does not live in One Madison building. D does not live in the same building as A or E and is flying a yellow coloured kite. B lives in One Madison building with only one more person and is flying a green kite. None in the Cayan Tower building flies a white kite. E does not fly a blue kite.
Q 8. Who lives in One Madison building?
- B, D”,
- A, C, E”,
- F, K”,
- A, D”,
Answer: 1
Solution 8:
Boy | A | B | C | D | E | F | K |
Building | Cayan Tower | One Madison | Cayan Tower | One Madison | Cayan Tower | The Shard | The Shard |
Kite | Blue | Green | Black | Yellow | Red | Pink | White |
From the table, we can see that B and D live in the Madison building.
Q 9. Who is flying the blue kite?
- D”,
- A”,
- C”,
- F”,
Answer: 2
Solution 9:
From the table, we can see that A flies the blue kite.
Q 10. Who flies the red kite?
- F”,
- K”,
- E”,
- A”,
Answer: 3
Solution 10:
From the table, we can see that E flies the red kite.
Q 11. Who stays in the Cayan Tower building?
- A, D”,
- F, K, D”,
- C, E, F”,
- A, C, E”,
Answer: 4
Solution 11:
From the table, we can see that A, C and E stay in the Cayan Towers
Q 12. What coloured kite is K flying?
- White”,
- Blue”,
- Black”,
- Yellow”,
Answer: 1
Solution 12:
From the table, we can see that K flies the white kite.
Directions (13 – 17): Read the following information carefully and answer the questions given below.
(i) A, B, C, D, E, F and G are sitting around a circle and facing the centre.
(ii) G is second to the left of C, who is to the immediate left of F.
(iii) A is third to the left of E.
(iv) B is between D and E.
Q 13. Which of the following is false?
- A is fourth to the right of E”,
- G is to the immediate right of D.”,
- F is third to the right of D.”,
- B is to the immediate left of D.”,
Answer: 3
Solution 13:
From the diagram, we can see that F is third to the right of D is false.
Q 14. Which of the following is true?
- C is fourth to the left of B.”,
- A is to the immediate right of G.”,
- D is second to the left of E.”,
- B is to the right of G.”,
Answer: 2
Solution 14:
From the diagram, we can see that A is to the immediate right of G.
Q 15. Which of the following pairs has the first person sitting to the immediate left of the second person?
- BE”,
- CA”,
- GD”,
- DG”,
Answer: 4
Solution 15:
From the diagram, we can see that DG is the answer.
Q 16. Which of the following pair has the middle person sitting between the remaining two?
- FCE”,
- EFB”,
- DEB”,
- None of these”,
Answer: 4
Solution 16:
From the figure, we can see that none of the combinations are right.
Q 17. Which of the following is the position of F?
- Fourth to the right of D”,
- To the immediate left of C”,
- Between A and E”,
- None of these”,
Answer: 1
Solution 17:
From the diagram, we can see that F is fourth to the right of D.
Directions (18 – 22): Fill in the blanks with the appropriate word.
Q 18. While that represents a departure from the previous US diplomatic efforts, which had always aimed to lead Israelis and Palestinians to negotiate a peace treaty between themselves under American ———-, this approach is not necessarily a bad idea.
- Auspices”,
- Antagonism”,
- Blockage”,
- Hindrance”,
Answer: 1
Q 19. The Palestinian authority disavowed at the ballot box in Gaza in 2006, run by aging leaders, and undermined by corruption has lost the ——– that it would need to make concessions.
- Dereliction”,
- Legitimacy”,
- Abomination”,
- Felony”,
Answer: 2
Q 20. An ———— could, in theory, overcome these obstacles. Moreover, Kushner’s close ties to Israel may paradoxically be a further asset.
- Agitator”,
- Instigator”,
- Arbitrator”,
- Partisan”,
Answer: 3
Q 21. History shows that winners of Geopolitical confrontations almost never voluntarily give up the fruits of their victory. Israel, a regional superpower with a post-industrial economy, nuclear weapons, and an ——— alliance with the US, clearly has the means to impose its will on a weak Palestinian adversary.
- Deviating”,
- Irresolute”,
- Turbulent”,
- Unwavering”,
Answer: 4
Q 22. Israel, therefore, holds the key to resolving the conflict. But that means ——- the Israeli public to accept the establishment of a foreign country, possibly an enemy just 15 kilometres from its capital.
- Persuading”,
- Disincentivise”,
- Hindrance”,
- Repulsion”,
Answer: 1
Directions (23 – 25): Rearrange the given 4 sentences in a proper sequence so as to form a meaningful paragraph
- Many countries flourished in the new environment. Poland, for example, installed a non-communist-led-government shortly before the Berlin Wall fell, and, after overcoming some early transition problems, moved smoothly toward NATO and the European Union.”,
- November 9, 1989, is a date my generation will never forget, and one that will forever be inscribed in human history. On that day nearly 30 years ago, the Berlin Wall fell.”,
- The break-up of Soviet bloc showed that Communism was to become the second great ideological failure of the twentieth century, following the demise of fascism a few decades earlier.”,
- Liberal capitalism and its main exponent, the United States, reigned supreme, seemingly destined to enjoy a long unchallenged hegemony.”,
Q 23. Which of the following is the third sentence?
- 4″,
- 1″,
- 2″,
- 3″,
Answer: 1
Q 24. Which of the following is the second sentence?
- 2″,
- 3″,
- 1″,
- 4″,
Answer: 2
Q 25. Which of the following is the first sentence?
- 4″,
- 3″,
- 2″,
- 1″,
Answer: 3
Q 1. Suppose A1, A2, A3, A4 and A5 are 5 companies. The profits made by A1, A2, and A3 are in the ratio 9:10:8. While profits made by A2, A4 and A5 are in the ratio 18:19:20. If A5 has made a profit of Rs 19 crore more than A1, then the total profit in rupees made by all 5 companies is:
- 213
- 675
- 349
- 438
Answer: D
Solution 1:
A1 : A2: A3 = 9:10:8 = (9✕18 : 10✕18: 8✕18) = 162: 180: 144
A2: A4: A5 = 18: 19: 20 = (18 ✕ 10: 19 ✕ 10: 20 ✕ 10) = 180: 190: 200
A1: A2: A3: A4: A5 = 162: 180: 144: 199: 200
200x – 162x = 38x
As per the question, 38x = 19 crore
Total of profit ratios
162 + 180 + 144 + 190 + 200 = 876
Hence total profit = 876 ✕ (19 / 38)
= 438 crore.
Q 2. The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:
- 65
- 39
- 20
- 55
Answer: A
Solution 2:
Since the number of girls and boys are not given, let us assume there are 100 boys.
As the number of girls are twice the number of boys, the number of girls are 200.
The total number of candidates appearing for the admission test is 300.
30 % of girls get admission, it means 60 girls out of 200 have got the admission.
45% of boys get admission, it means 45 boys out of 100 have got the admission.
Hence the total number of candidates who secured admission is 60 + 45 = 105
Number of candidates who did not secure admission = 300 – 105 = 195
Hence the percentage of students who did not get admission
= ( 195 / 300 ) ✕ 100
= 65 %
Q 3. Aman can complete a job in 10 days and Bhim can complete it in 8 days. Aman, Bhim and Kashi together can complete the job in 4 days and are paid a total remuneration of Rs 1000/-. If this amount is shared by them in proportion to their work, then Kashi’s share, in rupees, is
- 200
- 100
- 300
- 250
Answer: B
Solution 3:
It is better to avoid fractions and use fractions to percentage conversion method for faster calculation.
Aman can complete a job in 10 days implies
Aman’s 1-day job = 1/10 = 10 %
Bhim can complete a job in 8 days implies
Bhim’s 1-day job = ⅛ = 12.5 %
Aman, Bhim and Kashi can complete the same job in 4 days.
Hence the work done by all 3 of them in 1 day = ¼ = 25 %
Therefore the work done by Kamal in 1 day
= 25 – (10 + 12.5) = 25 – 22.5
= 2.5 %
The ratio of work done in 1 day by all 3 of them
= 10: 12.5: 2.5
= 4: 5: 1
Remuneration = Rs 1000/-
Share of Kashi = [ 1 / (4+5+1) ] ✕ 1000
= Rs 100/-
Q 4. 2 numbers are in the ratio of 16:13. If their HCF is 9, find the numbers.
- 119
- 137
- 117
- 127
Answer: C
Solution 4:
When the 2 numbers are in ratio, then the numbers are 16x and 13x
Here X is the HCF.
Hence the numbers are
16 ✕ 9 = 144
and 13 ✕ 9 = 117
Q 5. Four steel rods of lengths 84 cm, 112 cm, 126 cm, 154 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
- 14
- 24
- 54
- 34
Answer: D
Solution 5:
Each steel rod that is cut needs to be of a maximum possible length and of same length such that we can get the maximum number of pieces.
To make sure the above condition is satisfied we need to find HCF of the above lengths.
To find HCF of multiple numbers, we find the prime factors of the individual numbers and then multiply the common prime factors with the least powers.
84 = 2^{2} ✕ 3 ✕ 7
112 = 2^{4} ✕ 7
126 = 2 ✕ 3^{2} ✕ 7
154 = 2 ✕ 7 ✕ 11
The common factors are 2 and 7. The least power of 2 is 1 and the least power of 7 is 1.
Hence,
HCF = 2 ✕ 7 = 14
Therefore the number of pieces = ( 84 + 112 + 126 + 154 ) / 14
= 476 / 14
= 34
Q 6. 3 sets of French, Russian, Japanese books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subject wise and the height of each stack is the same. Total number of stacks will be
- 14
- 25
- 56
- 77
Answer: A
Solution 6:
To find the maximum number of books that can be stacked, such that each stack has equal number of books, we need to find the HCF of 336, 240, and 96 books.
To find the HCF of multiple numbers we need to find the common prime factors and multiply the common prime factors with their least powers.
Prime factors of numbers are given below
336 = 2^{4} ✕ 3 ✕ 7
240 = 2^{4} ✕ 3 ✕ 5
96 = 2^{5} ✕ 3
Common prime factors are 2 and 3.
Least power of 2 is 4 and the least power of 3 is 1.
Hence the HCF of 336, 240, 96 is
2^{4} ✕ 3 = 48.
Hence in each stack, we can keep 48 books.
To find the maximum number of stacks, with each stack containing the same number of books i.e. 48 is given by
( 336 + 240 + 96 ) / 48
= 14
Hence there are a total of 14 stacks with each stack consisting of a maximum 48 books.
Q 7. A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in the month of June beginning with a Sunday?
- 321
- 456
- 285
- 130
Answer: C
Solution 7:
As the month begins with Sunday, there are 5 Sundays in the month of June.
Hence the total number of visitors in the month of June
= 510 ✕ 5
= 2,550
On the remaining 25 days, there are 240 visitors on each day.
Hence the total number of visitors on the remaining days
= 240 ✕ 25
= 6,000
Total number of visitors in the month = 2500 + 6000 = 8500
Therefore the average number of visitors in the month
= 8550 / 30
= 285
Q 8. There are 4 consecutive odd numbers (x_{1}, x_{2}, x_{3}, x_{4}) and 3 consecutive even numbers (y_{1}, y_{2},y_{3}). The average of the odd numbers is 6 less than the average of even numbers. If the sum of the 3 even numbers is 16 less than the sum of the four odd numbers, what is the average of x_{1}, x_{2}, x_{3}, x_{4}?
- 42
- 32
- 72
- 82
Answer: B
Solution 8:
Average of the 4 odd numbers is 6 less than average of 3 even numbers
(X_{1} + x_{2} + x_{3} + x_{4}) / 4 = [ (y_{1}+ y_{2}+ y_{3}) / 3 ] – 6
Simplifying the above equation we get,
3x_{1} + 3x_{2} + 3x_{3} + 3x_{4} = 4y_{1}+ 4y_{2}+ 4y_{3} – 72
3 (x_{1} + x_{2} + x_{3} + x_{4}) = 4 (y_{1}+ y_{2}+ y_{3} – 18) ——- Equation (1)
Also, the question says
x_{1} + x_{2} + x_{3} + x_{4} – 16 = y_{1}+ y_{2}+ y_{3}
x_{1} + x_{2} + x_{3} + x_{4} = y_{1}+ y_{2}+ y_{3} + 16 ——Equation (2)
Substitute the value of Equation (2), x_{1} + x_{2} + x_{3} + x_{4 } in Equation (1).
Hence we get,
3 (y_{1}+ y_{2}+ y_{3} + 16) = 4 (y_{1}+ y_{2}+ y_{3} – 18)
Solving the above equation we get,
y_{1}+ y_{2}+ y_{3} = 48 + 72
= 112
Substituting the above value in equation (2)
Now, x_{1} + x_{2} + x_{3} + x_{4 } = 112 + 16
= 128
Average of x_{1} + x_{2} + x_{3} + x_{4} = 128 / 4
= 32
Q 9. A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. The number is
- 27
- 45
- 54
- 56
Answer: A
Solution 9:
Let the number be 10a + b
Sum of its digits can be represented as a + b
As per the question,
10a + b = 3 (a + b)
7a = 2b
So, b = (7/2) a
10a + b + 45 = 10b + a
9a + 45 = 9b
9a + 45 = 9 (7/2) a
18a + 90 = 63 a
45a = 90
Hence, a = 2
Substituting the value of a, we get b = 7
Hence the number is 27.
Directions (10-14): Study the information carefully to answer the questions.
A, C, E, G, F, L and S are seven people who studied in 3 management institutes X, Y and Z. They had opted for one out of the three specializations – Marketing, Finance, and Operations – with at least two of them in each specialization. No two persons have the same combination of institute and specialization.
The Marketing specialist from Institute Y earns the maximum. C studied in an institute Z with Operations specialization and earns more than only A and G. E studied in institute X with Marketing and earns less than only F and S. L studied in institute Z with Finance and earns more than C but less than E. S studied in institute X with Finance Specialization. G, an Operations specialist, studied in institute Y and is not the least earner among them. A is the only Finance specialist from one of these institutes among them.
Q 10. In which of the institutes did A study?
- X
- Y
- Z
- Y or Z
Answer: B
Solution 10:
Earnings (Descending order) | Person | Institute | Specialization |
1 | F | Y | Marketing |
2 | S | X | Finance |
3 | E | X | Marketing |
4 | L | Z | Finance |
5 | C | Z | Personnel |
6 | G | Y | Personnel |
7 | A | Y | Finance |
From the above table, we can find that A studied in institute Y.
Q 11. What is F’s specialization?
- Operations
- Marketing
- Finance
- Data inadequate
Answer: B
Solution 11:
From the table, we can see that F’s specialization is in Marketing.
Q 12. Which of the following combinations of the institute – individual – specialization is not correct?
- X – G – Operations
- X – E-Marketing
- Y – A – Finance
- Z – L – Finance
Answer: A
Solution 12:
From the table, we can see that option 1 is incorrect, the correct answer is Y – G – Operations.
Q 13. Whose income is the 2nd highest among them?
- S
- E
- F
- None of these.
Answer: A
Solution 13:
From the table, we can see that S is the 2nd highest earner.
Q 14. How many of them earn more than C?
- 2
- 4
- 5
- 3
Answer: B
Solution 14:
From the table, we can see that 4 of them earn more than C.
Q 15. A man is facing North – West. He turns 90^{o} in the clockwise direction and then 135^{o} in the anti-clockwise direction. Which direction is he facing now?
- West
- South
- North
- East
Answer: A
Solution 15:
As per the first change of direction, when the man turns 90^{0} in the clockwise direction he starts facing North-East direction, in other words, 45^{0 } to the right of North West is North and further 45 degrees from North is North-East direction.
In the 2nd statement, he turns 135^{0} in the Anti-clockwise direction.
135 is nothing but 90 + 45.
So when he initially turns 90^{o} in the anti-clockwise direction from the current North-East direction, he returns back to his initial position and when he moves further 45 degrees (so that he completes 135 degrees in total) he will be facing West direction. From North West to West direction it is 45 degrees. So overall he has covered 135 degrees from North-East direction and he ends up facing West direction.
Directions (16 – 20): Rearrange the given 5 sentences in a proper sequence so as to form a meaningful paragraph
- According to Turkish Official estimates, Turkey currently hosts about 3.6 million Syrian refugees and has spent nearly US $ 4 Billion on their Housing and Welfare. While underlining that talks with the US on establishing a safe zone is still under progress, Erdogan expressed Turkey’s determination to continue with the plan.
- Turkey launched an operation, a military excursion into North-Eastern Syria to establish a safe zone with the objective of preventing the Syrian Democratic Forces (SDF) from controlling areas along the Turkish-Syrian border.
- This is part of Turkey’s long-standing goal to have a military presence in Syria to neutralise the alleged terror corridor run by the SDF. Ankara has been opposed to the formation of an autonomous Kurdish region in North-Eastern Syria because of insurgency led by the Kurdistan Workers Party.
- In his address at the 74th Session of the United Nations General Assembly on September 24, President Recep Tayyip Erdogan gave a detailed account of Turkeys plans to establish the safe zone, along the Turkeys South Eastern Border.
- According to Erdogan, the safe zone will be 480 kilometres long and 30 kilometres deep inside Syria. He argued that the safe zone east of River Euphrates will be able to house nearly 2 million Syrian refugees who were forced to flee to Turkey after 2011.
Q 16. Which of the following is the fifth sentence?
- 2
- 3
- 4
- 1
Answer: D
Q 17. Which of the following is the 1st sentence?
- 1
- 4
- 2
- 5
Answer: C
Q 18. Which of the following is the second sentence?
- 4
- 3
- 5
- 1
Answer: B
Q 19. Which of the following is the third sentence?
- 4
- 1
- 3
- 2
Answer: A
Q 20. Which of the following is the fourth sentence?
- 3
- 1
- 2
- 5
Answer: D
Directions (21 – 25): Fill in the blanks with the appropriate word.
Q 21. It was the West’s ——– to protect the flow of oil to the global economy.
- Barring
- Proscription
- Interdiction
- Prerogative
Answer: D
Q 22. Trump, by contrast, has no strategy, and wants to disguise America’s retreat from the region,currently demonstrated in Syria by the open betrayal of the Kurds, with militant ——- and massive arms exports to US partners and allies in the Gulf.
- Unadorned
- Plain speaking
- Rhetoric
- Restrained
Answer: C
Q 23. For its part, Saudi Arabia, the regions wealthy, predominantly Sunni power, has long harbored ambitions for regional ———–.
- Subservice
- Hegemony
- Subjugation
- Feebleness
Answer: B
Q 24. For the past few years, Iran and Saudi Arabia has been waging a disastrous proxy war in Yemen, resulting in a massive toll of civilian casualties and a humanitarian ———
- Benediction
- Catastrophe
- Benison
- Miracle
Answer: B
Q 25. A midnight attack without warning raises ——- questions.
- Obvious
- Inconclusive
- Fuzzy
- Subtle
Answer: A
Q.1 In a certain code language, ‘how many goals scored’ is written as ‘5 3 9 7’, ‘many more matches’ is written as ‘9 8 2’ and ‘he scored five’ is written as ‘1 6 3’. How is goals’ written in that code language?
- 5
- 7
- 5 or 7
- Data inadequate
- None of these
Answer: (3)
Q.2 How many meaningful English words can be made with the letters DLEI using each letter only once in each word?
- None
- One
- Two
- Three
- More than three
Answer: (5)
Q.3 Among B, C, D, E and F, all having different weights, D is heavier than only B and D is lighter than C and F. Who among them is the heaviest?
- C
- F
- D
- Data Inadequate
- None of these
Answer: (4)
Q.4 If ÷ means +, – means x, x means ÷ and means -, then 15 – 8 x 6 ÷ 12 + 4 = ?
- 20
- 28
- 8
- 2
- None of these
Answer: (2)
Q.5 Town E is towards east of Town G. Town C is towards north of Town E. Town I is towards south of Town C. Towards which direction is Town I from Town G?
- East
- Southeast
- Northeast
- Data Inadequate
- None of these
Answer: (4)
Solution Q.1 – Q.5
Solution 1: (3) From the given information, the code for many is 9 and that for scored is 3. So, the code for goals is either 5 or 7
Solution 2: (5) The words formed by DLIE are LIED, DELI, DIEL and IDLE
Solution 3: (4) From the given information, either C or F is the heaviest
Solution 4: (2) By replacing the symbols with the correct ones, the expression becomes
15 x 8 ÷ 6 + 12 -4 = 28
Solution 5: (4) Since Town I is in the south of Town C, it can be either below E or between C and E. So, we cannot determine I’s position exactly.
Directions (Q.6 – Q.9): Following are the steps of an input. Rearrange them and answer the questions.
- mettle offed archaic bleach kettle
- archaic bleach kettle mettle offed
- kettle mettle offed archaic bleach
- offed archaic bleach kettle mettle
- kettle mettle bleach offed archaic
Q.6 Which of the following is step III?
- A
- B
- C
- D
- E
Answer: (1)
Q.7 Which of the following is the first from the right end of step II?
- Barrage
- Kettle
- Mettle
- Bleach
- None of these
Answer: (2)
Q.8 Which of the following is step V?
- A
- B
- C
- D
- E
Answer: (4)
Q.9 Which of the following is step IV?
- A
- B
- C
- D
- E
Answer: (4)
Solution: The words are are arranged by moving them in alphabetical order from right to left.
Step I: kettle mettle bleach offed archaic
Step II: kettle mettle offed archaic bleach
Step III: mettle offed archaic bleach kettle
Step IV: offed archaic bleach kettle mettle
Step V: archaic bleach kettle mettle offed
6. (1) Step III in the above arrangement “mettle offed archaic bleach kettle”
7. (2) Step II in the above arrangement is “kettle mettle offed archaic bleach”
8. (4) Step V in the above arrangement is “archaic bleach kettle mettle offed”
9. (4) Step IV in the above arrangement is “offed archaic bleach kettle mettle”
Directions Q.10 – Q.11: Study the following table carefully to answer the questions that follow.
The table represents the total number of students playing different sports i.e., Football, Cricket, Badminton, Tennis and Volleyball across eight institutes, i.e., P, Q, R, S, T, U, V and W.
Sports | Institutes | |||||||
P | Q | R | S | T | U | V | W | |
Football | 500 | 410 | 280 | 340 | 610 | 510 | 440 | 650 |
Cricket | 480 | 460 | 340 | 440 | 640 | 550 | 260 | 420 |
Badminton | 420 | 360 | 480 | 560 | 540 | 450 | 350 | 340 |
Tennis | 520 | 320 | 520 | 480 | 510 | 310 | 680 | 640 |
Volleyball | 360 | 260 | 410 | 380 | 420 | 660 | 480 | 620 |
Q.10 The number of students playing Cricket in Institute Q forms what percentage of the total number of students in Institute R?
- 20%
- 18%
- 22.6%
- 24%
- 28%
Answer: (3)
Solution 10: (3) Number of students playing Cricket in institute Q = 460
Total number of students in institute R = 280 + 340 + 480 + 520 + 410 = 2030
Therefore, the number of students playing cricket in institute Q as a percentage of the total number of students in the institute R is calculated as:
460/2030x 100 = 22.6%
Q.11 The number of students playing football in Institute Q forms what percentage of the total number of students in Institute Q?
- 21.9%
- 20%
- 32%
- 36%
- 28%
Answer: (1)
Solution 11: (1)
Number of students playing Football in institute Q = 500
Total number of students in institute P = 500 + 480 + 420 + 520 + 360 = 2280
Therefore, the number of students playing Football in institute Q as a percentage of the total number of students in the institute Q is calculated as:
500/2280x 100 = 21.9%
Directions Q.12 – Q.14: What will come in place of the question mark (?) in the given series?
Q.12 125, 128, 119, 146, 65, (?)
- 300
- 308
- 280
- 310
- 250
Answer: (2)
Solution 12: (2) The pattern of the series is
- 128 – 125 = 3^{1}
- 119 – 128 = -9 = 3^{2} (ignore the negative sign)
- 146 – 119 = 27 = 3^{3}
- 65 – 146 = -81 = 3^{4} (ignore the negative sign)
Now, 3^{5} = 243
Therefore, 243 + 65 = 308
Hence, the required number = 308
Q.13 24, 12, 12, 18, (?), 90
- 36
- 38
- 40
- 26
- 32
Answer: (2)
Solution 13: (2) The pattern of the series is
- 24 x ½ = 12
- 12 x (½ + ½ ) = 12
- 12 x (1 + ½ ) = 12 x = 18
- 18 x ( + ½ ) = 18 x 2 = 36
- 36 x (2 + ½ ) = 36 x () = 90
Q.14 33, 39, 57, 87, 129, (?)
- 180
- 183
- 176
- 150
- 154
Answer: (2)
Solution 14: (2) The pattern of the number series is
- 33 + 6 = 39
- 39 + 18 (= 6 + 12) = 57
- 57 + 30 (=18 +12) = 87
- 87 + 42 (=20 + 12) = 129
- 129 + 54 (=42 + 12) = 183
Directions Q.15 – Q.16: In each of these questions, two equations I and II are given. You have to solve the equations to find the relation between P and Q.
Mark your answer as:
- If P > Q
- If P ≥ Q
- If P < Q
- If P ≤ Q
- If P = Q
Q. 15 I. P^{2} – 12P + 32 = 0
II. Q^{2} – 13Q + 36 = 0
Answer: (4)
Solution 15: (4) Statement I ⇒ P^{2 }– 4P – 8P + 32 = 0
⇐ P (P – 4) – 8 (P- 4) =0
⇐ (P – 4) (P – 8) = 0
Therefore, P = 4 or P = 8
Statement II ⇒ Q^{2} – 4Q – 9Q + 36 = 0
⇐ Q(Q – 4) – 9(Q – 4) = 0
⇐ (Q – 4) (Q – 9) = 0
Therefore, Q = 4 or Q = 9
Hence, P ≤ Q
Q. (16) I. P^{2} – 10P + 24 = 0
II. 3Q^{2} – 19Q + 28 = 0
Answer: (2)
Solution 16: (2) Statement I ⇒ P^{2} – 4P – 6P + 24 = 0
⇐ P(P – 4) – 6(P – 4) = 0
⇐ (P – 4) (P – 6) = 0
Therefore, P = 4 or P = 6
Statement II ⇒ 3Q^{2} – 12Q – 7Q + 28 = 0
⇐ 3Q(Q – 4) – 7(Q – 4) = 0
⇐ (3Q – 7) (Q – 4) = 0
Therefore, Q = 7/3 or Q = 4
Hence, P ≥ Q
Q. 17 A invests 10% i.e., 2500 of her monthly salary in mutual funds. Later A deposited 16% of her monthly salary in fixed deposit also. 8% of A’s monthly salary is invested on SIP. What is the total annual amount invested by A?
- 12,000
- 10,000
- 10,200
- 15,000
- 12,500
Answer: (3)
Solution 17: (3)
Monthly salary of A = Rs.= 25000
Monthly investment of A in percent = 10% + 16% + 8% = 34%
Therefore, annual investment of A = Rs. [12 x (34% of 25000)]
= Rs. (12 x 34 x 250)
= Rs. 10,200
Directions Q.18 to Q.22: Read each sentence to find any grammatical error(s). If there are any it will be one part of the sentences. Mark that part as your answer. If the sentence is correct mark the option 5 (No error) as your answer. (Ignore any punctuation errors as such).
Q.18 Many an (1) engineer has filled up (2) / this forma a (3) / long time ago. (4) / No error (5)
Answer: (5)
Q.19 As Karan and Sudha watched (1) / the football match, which (2) / were being played in Canada, the (3) / man robbed the whole house. (4) / No error (5)
Answer: (3)
Q.20 Each group were (1) / given a separate tent (2) / and some tools to (3) / make the required project. (4) / No error (5)
Answer: (1)
Q.21 The meeting was commenced (1) / with a detailed discussion (2) / on the projects (3) / inside the pipeline. (4) / No error (5)
Answer: (4)
Q.22 As soon as the telegram (1) / reached Nanda’s house that her (2) / family set out to rescue (3) / her from the situation. (4) / No error (5)
Answer: (2)
Solution Q.18: (5) There is no error in this sentence ‘Many a/an’ is used as a determiner before a singular noun that takes a singular verb.
Solution Q.19: (3) Singular subject takes singular verb. ‘Football match’ is a singular subject that will take the verb ‘was’ not ‘were’.
Solution Q.20: (1) The determiner ‘each’ is always followed by a singular noun and a singular verb
Solution Q.21: (4) The idiom used is incorrect. The correct idiom is ‘in the pipeline’, which means in the process or que
Solution Q.22: (2) ‘As soon as’ does not require ‘that’. So ‘that’ will have to be omitted from the sentence to make it grammatically correct.
Directions for Q.23 – Q.25: In each sentences there are five sentences. The sentence labelled A is in the correct place. The four that follow are labelled B, C,D and E and need to be arranged in the logical order to form a coherent passage. From the given options,choose the most appropriate option.
Q.23
(A) Hard times hit the most vulnerable sections of a society
(B) The crisis, as the UNFPA report “Reaching Common Ground: Culture , Gender and Human Rights”
(C) Two recently published global studies are timely reminders that gender inequalities, which persist in varying degrees across the world, are a dampener on economic growth, and that they should not be overlooked in the looming global economic downturn
(D) The inequalities are shocking. Nearly 60 percent of the world’s one billion poorest people are women and girls 66% of adult illiterates are women and 70% of the out-of-school children are girls.
(E) The reposts, one by the United Nations Population Fund (UNFPA), and the other by the World Economic Forum (WEF), differ in their approach to this global reality, but agree with the point that there are compelling advantages flowing from the empowerment of women.
- BECD
- DCEB
- CEDB
- CEBD
- EFBD
Answer: (4)
Q.24
(A) The fall in the external value of the rupee in relation to the dollar has been overshadowed by catastrophic events in the international financial markets
(B) The fast-paced developments in the US and other developed markets markets have important consequences for the emerging financial markets such as India’s
(C) The Central Banks and governments around the world have been focussing exclusively on the unfolding financial sector crisis originating from the United States. Although it is more than a year since the sub prime crisis surfaced, it assumed mencacing proportions only recently as seen in the failures of iconic financial institutions in the US prompting monetary authorities to resort to some bold unconventional measures to save some of them
(D) India stock market indices, along with those of most of the stock markets of Asia, declined sharply, although they would recover later
(E) The extreme loss of investor confidence, coupled with serious disruption in the international money markets, has caused a flight of capital from emerging markets in search of safety
- CBED
- CEDB
- BCDE
- CBDE
- BECD
Answer: (1)
Q.25
- It may be difficult for us to imagine how the earth, which appears to us to be a solid mass of complexly interrelated parts, may be having an intention to purify and can be undergoing a process we normally associate with human beings on a spiritual path.
- The ‘great purification’ of the earth has been spoken of by the Hopi and other indegenous people as a prelude to a great transition of life and consciousness that the planet shall go through. This transition has also been prophesied within other ancient traditions as well as by individual seers
- Today, in midwest United States where massive flooding is taking place, and not too long ago in the West where fires raged out of control or in the South where hurricanes took a heavy toll on the populace, weather patterns have become quite extreme.
- And even if it is true of the planetary body, we may well wonder how this happens and how it can affect weather patterns.
- The purification to which those ancient ones refer is happening all around us. It is revealed in the altered weather patterns that are becoming commonplace around the globe.
- BEDC
- DBEC
- BDEC
- DEBC
- DCBE
Answer: (3)
Solution Q.23 to Q.25
Solution 23: Choice (4) is the logical sequence as Statement C elaborates on what is stated in A by saying that the ‘hard times’ refers to the global economic downturn and the ‘vulnerable sections’ are those affected by the ‘gender inequalities’ referred to in C.
Solution 24: Statement C follows A as it elaborates on the ‘calamitous events in the international financial markets’ – mentioned in A. Hence CBED is the correct sequence. (1)
Solution 25: B follows A linked by the reference to purification. Iti s a more generalised statement than D and so a better one to follow A. D follows B, ‘it’ referring to the purification and it introduces the idea of weather pattern which are continued in E and C. Thus BDEC is the correct sequence.(3)
Directions (Q.1 – Q.8): Study the following information and answer the following questions
K, L, M, N, O, P, Q and R are sitting around a circular table, facing the centre. Each of them was born in a different year – 1971, 1975, 1979, 1980, 1981, 1984, 1985 and 1990 – but not necessarily in the same order.
N is sitting second to the right of L. M is sitting third to the right of K. M and K were born before 1980. Only the one born in 1984 is sitting exactly between K and L. M, who is the eldest, is not an immediate neighbour of K or N. S is older than only N. S is sitting second to the left of Q. Q is not an immediate neighbour of M. K is younger than M. L was born before P.
Q.1 Who is the second oldest in the group?
- K
- M
- L
- Q
- None of these
Answer: (2)
Q.2 Who is sitting third to the right of P?
- The one born in 1979
- The one born in 1980
- The one born in 1985
- The one born in 1984
- None of these
Answer: (1)
Q.3 In which year was S born?
- 1979
- 1975
- 1980
- 1985
- None of these
Answer: (4)
Q.4 Which of the following statements is true regarding L?
- L is sitting fourth to the right of S
- The one who was born in 1975 is on the immediate left of L
- L is younger than S
- There are four persons sitting between O and L
- None of these
Answer: (5)
Q.5 In which year was P born?
- 1984
- 1989
- 1980
- 1975
- 1981
Answer: (5)
Q.6 Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to the group?
- Mica
- Zinc
- Iron
- Chlorine
- Aluminium
Answer: (4)
Q.7 If it is possible to make only one meaningful word with the first, the third, the fifth and the eight letters of the word SHAREHOLDING. Which of the following will be the second letter of that word? If no such word can be made, give ‘X’ as the answer and if more than one such word can be made, give ‘Y” as the answer.
- L
- E
- S
- X
- Y
Answer: (3)
Q.8 Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
- 18
- 24
- 36
- 34
- 26
Answer: (5)
Solution Q.1 – Q.8:
Solution 1: (2) M is the second oldest in the group and as born in 1975
Solution 2: (1) K is sitting third to the right of P and was born in 1979
Solution 3: (4) S was born in 1985
Solution 4: (5) L is sitting third to the right of S. The one who was born in 1975 (M) is on the immediate right of L. S is younger than L. Only three persons (P, N and K) are sitting between O and L.
Solution 5: (5) P was born in 1981
Solution 6: (4) Except chlorine, all other are solids
Solution 7: (3) Among all the given numbers, only 36 is a perfect square
Solution 8: (5) Human blood is red in colour and according to the question red means violet.
Directions Q.9 – Q.10: Study the following information and answer the following questions
Q.9 What will be the remainder (37^{35 }+ 36) is divided by 38?
- 28
- 11
- 23
- 35
- 18
Answer: (4)
Q.10 Let A be the greatest number that divides 1300, 4650 and 6325, leaving the same remainder in each case. What is the sum of the digits in A?
- 8
- 19
- 22
- 27
- 34
Answer: (2)
Q.11 The first number is twice the second number and half the third number. The average of these numbers is 35. What is the value of the smallest numbers?
- 15
- 30
- 45
- 60
- 75
Answer: (1)
Solution 9: (4) If n is an odd number, then (x^{n} + 1) is always divisible by (x + 1)
Therefore, (37^{35 }+ 1) + 35, therefore the required remainder is 35
Solution 10: (2) The greatest number that divides 1300, 4650 and 6325, leaving the same remainder in each case = HCF 0f (4650 – 1300), (6325 – 4650) and (6325 – 1300) = HCF of 3350, 1675 and 5025 = 1675 = A
Therefore, the required sum of digits of A = 1 + 6 + 7 + 5 = 19
Solution 11: (1) Let three numbers = x, y and z According to the question,
X = 2y = ½ z
Average of three numbers = 35; therefore,
X + y + z/ 3 = 35
X + 2x + x/2 = 105
X = 30
Y = 15 = Smallest number
Z = 60
Directions Q.12 – Q.13: In each of the following number series, only one is wrong. Find out the wrong number.
Q.12 454, 327, 648, 524, 842, 713, 1036, 918
- 327
- 648
- 524
- 842
- 713
Answer: (5)
Q.13 4, 8, 16, 30, 64, 128, 256
- 8
- 16
- 30
- 64
- 128
Answer: (3)
Solution 12: (5) The given series is formed by combining two series.
The first series = 454, 648, 842, 1036
In the first series, each number is 194 more than the previous numbers.
The second series = 327, 524, 713, 918
In the second series, each number is 197 more than its previous number except 713
Solution 13: (3) The given series is an increasing series in which each term is twice the previous number except 30. It should be 32 in place of 30
Directions Q.14 to Q.16: Each of the questions is followed by two arguments numbered I and II. You are to decide which one is strong and which is weak. Mark the answer:
- If argument I is strong”,
- If argument II is strong”,
- If neither I nor II is strong”,
- If both I and II are strong”,
- Data inconclusive”,
Q.14 Should all the elected legislative members be put through compulsory for running the government?
Arguments:
I. Yes, it will certainly be helpful
II. No, people elect only those individuals who are matured enough to hold the office.
Answer: (1)
Q.15 Should primary education be made free in India?
Arguments:
I. Yes, as it is the duty of a welfare state to impart primary education
II. No, as the number of primary schools are inadequate to accommodate all.
Answer: (3)
Q.16 Should rural banks be abolished
Arguments:
I. Yes, as they are not up to the mark
II. No, because they play a crucial role in developing villages
Answer: (2)
Solution Q.14 to Q.16:
Solution 14: Elected legislative members undergoing compulsory training will be helpful. So only argument I is strong. Thus (1) is the answer.
Solution 15: Neither of the arguments is strong. So (3) is the answer
Solution 16: Rural banks play a crucial role in the development of villages. So argument II is strong. Thus (2) is the answer.
Directions Q.17 to Q.21: Read each sentence to find any grammatical error(s). If there are any it will be one part of the sentences. Mark that part as your answer. If the sentence is correct mark the option 5 (No error) as your answer. (Ignore any punctuation errors as such).
Q.17 Many an (1) engineer has filled up (2) / this forma a (3) / long time ago. (4) / No error (5)
Answer: (5)
Q.18 As Visisht and Priyanka watched (1) / the football match, which (2) / were being played in Italy, the (3) / man robbed the whole house. (4) / No error (5)
Answer: (3)
Q.19 Each group were (1) / given a separate tent (2) / and some tools to (3) / make the required project. (4) / No error (5)
Answer: (1)
Q.20 The meeting was commenced (1) / with a detailed discussion (2) / on the projects (3) / inside the pipeline. (4) / No error (5)
Answer: (4)
Q.21 As soon as the telegram (1) / reached Nanda’s house that her (2) / family set out to rescue (3) / her from the situation. (4) / No error (5)
Answer: (2)
Solution Q.17: (5) There is no error in this sentence ‘Many a/an’ is used as a determiner before a singular noun that takes a singular verb.
Solution Q.18: (3) Singular subject takes singular verb. ‘Football match’ is a singular subject that will take the verb ‘was’ not ‘were’.
Solution Q.19: (1) The determiner ‘each’ is always followed by a singular noun and a singular verb
Solution Q.20: (4) The idiom used is incorrect. The correct idiom is ‘in the pipeline’, which means in the process or que
Direction for Q.22 to Q.24: Each question contains a pair of CAPITALISED words followed by f pairs of words. Choose the pair of words that does not express a relationship similar to the one expressed by the capitalized pair.
Solution Q.21: (2) ‘As soon as’ does not require ‘that’. So ‘that’ will have to be omitted from the sentence to make it grammatically correct.
Q.22 FELINE : CATS
- Equine : Horses
- Wolverine : Wolves
- Ovine : Sheep
- Cervine : Deer
- Bovine: Cow
Answer: (2)
Q.23 TYRANT : COMPASSION
- Martinet : Discipline
- Egotist : Humility
- Reprobate : Ethics
- Dictator : Humanity
Answer: (1)
Q.24 CLIMAX : CLIMATIC
- Orgy : Orgiastic
- Periphrasis : Periphrastic
- Apocalypse : Apocalyptic
- Viceroy : Vice royal
- Titan: Titanic
Answer: (4)
Solution 22: (2) The word wolverine refers to a glutton and is not an adjective which means of or like a wolf. Hence choice 2 does not express a relationship seen in the other pairs
Solution 23: (1) A martinet (a disciplinarian) is associated with discipline and not one who is lacking in discipline and hence choice (1)
Solution 24: (4) The adjective form of the noun viceroy is vice regal and not vice royal
Q.25 In each of the following number series, only one is wrong. Find out the wrong number.
- 4
- 9
- 16
- 24
- 36
Answer: (4)
Solution 25: If you take a careful look at the above series, you will see that each number is the square of its position in the series. So 24 is not a square.
Q.1 What is the ratio between Ankit monthly expenses on petrol to Mary’s monthly expenses on grocery?
- 50:23
- 3:5
- 5:4
- 23:50
- None of the above
Answer: D
Solution 1:
Ankit’s monthly expenses on petrol = 9200
Mary’s monthly expenses on grocery = 20,000
Ratio = 9200 : 20000 = 23:50
Q 2. If Amar’s’s salary increases by 25%, what will be his new salary?
- 77,500
- 66500
- 33400
- 32130
- 56000
Answer: A
Solution 2:
Alan’s current salary = Rs.62,000
After increasing Alan’s salary = 125% of 62000
= Rs. 77,500
Q.3 Pranav, Vinit and Anup begin to jo around a stadium. They complete their revolutions in 45 seconds, 54 seconds and 36 seconds respectively. After how many seconds will they be together at the starting point?
- 360
- 600
- 540
- 450
- None of these
Answer: C
Solution 3: Time taken by Pranav, Vinit and Anup to be together at the starting point
= LCM of 45, 54 and 36 seconds
= 3 x 3 x 2 x 5 x 3 x 2 = 540 seconds
Q.4 12959.998 ÷ 18.010 = ?
- 840
- 990
- 570
- 680
- 720
Answer: E
Solution 4: ? = 12959.998 ÷ 18.010
= 12960/18 = 720
Directions Q.5 – Q.8: Answer the following questions by selecting the most appropriate option
Q.5 What will be remainder when (37^{35 }+ 36) is divided by 38?
- 28
- 23
- 11
- 35
- 18
Answer: D
Solution 5: If n is an odd number, then ( x^{n }+ 1) is always divisible by (x + 1)
Therefore, (37^{35 }+ 1) will be divisible by 38
(37^{35 }+ 36) = (37^{35} + 1) + 35, therefore the required remainder is 35
Q.6 Let A be the greatest number that divides 1300, 4650 and 6325, leaving the same remainder in each case. What is the sum of the digits in A?
- 8
- 19
- 22
- 27
- 34
Answer: B
Solution 6: The greatest number that divides 1300, 4650 and 6325, leaving the same remainder in each case = HCF pf (4650 – 1300), (6325 – 4650) and (6325 – 1300) = HCF of 3350, 1675 and 5025 = 1675 = A
Therefore, the required sum of digits of A = 1 + 6 + 7 + 5 = 19
Q.7 If the average of a, b, c, d, e and f is 18, then what will be the average of a/5, b/5, c/5, d/5, e/5 and f/5?
- 3
- 3.6
- 4
- 4.5
- None of these
Answer: B
Solution 7: It is already mentioned in the text of this module that if the average of X_{1}, X2, ………., X_{n}/ a is X/a
Therefore, the average of a/5. b/5, c/5, d/5, e/5 and f/5 = 18/5 =3.6
Q.8 The average height of 50 students is 170 cm. On a particular day, it was found that four students were absent and the average height of remaining 46 students is 168 cm. Find the average height of absent students.
- 190 cm
- 191 cm
- 192 cm
- 193 cm
- 194 cm
Answer: D
Solution 8: Average height of 50 students = 170 cm
Sum of their heights = 170 x 50 = 8500 cm
Average height of 46 students = 168
Sum of their heights = 168 x 46 = 7728
Sum of heights of 4 absent = Sum of heights of 50 students – Sum of heights of 46 students
= 8500 -7728
= 772 cm
Therefore, average height of 4 students = 772/4 = 193 cm
Q.9 A railway ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Bangalore to Kochi costs ₹ 216 and one full reserved and one half reserved first class tickets cost ₹ 327. What is the basic first class full fare and what is the reservation charge?
- ₹ 105, ₹ 6
- ₹ 216, ₹ 12
- ₹ 210, ₹ 6
- ₹ 210, ₹ 12
- ₹ 215, ₹ 15
Answer: C
Solution 9: Let the full fare be ₹ x and the reservation charge be ₹ y per ticket.
Then, x + y = 216
(i) 3/2x + 2y = 327
(ii) 3x + 4y = 654
By multiplying (i) by 3 and subtracting from (ii), we get: y = 6. Putting y = 6 in (i), we get: x =210
Q 10. 6 years ago, the ratio of the ages of Rajat and Karan is 7:6. Present age of Kunal is 10 years more than one – sixth of Karan’s present age. Find the ratio of present age of Karan and Kunal if Rajat’s age after 6 years is 40 years.
- 3:2
- 1:2
- 3:4
- 2:3
- 2:1
Answer: E
Solution 10:
Rajat’s age after 6 years = 40 years
Rajat’s present age = 40-6 = 34 years
Ratio of ages of Rajat and Karan 6 years ago = (Rajat – 6) / (Karan – 6) = 7:6
⟹28 / (Karan – 6) = 7:6
⟹Karan – 6 = (28×6) / 7
⟹ Karan – 6 = 24
⟹ Karan’s present age = 30 years
Present age of Kunal = (⅙ × 30) + 10 = 15 years
Ratio of Karan and Kunal’s present age = 30:15 = 2:1
Direction (Q.11 – Q.15): Study the information and answer the following questions
Six persons D, E, F, G, H and I are standing in a straight line facing north but not necessarily in the same order. E is standing second to the right of G, D is standing fourth to the left of I and I is not standing on the extreme end of the line. F is standing second to the right of E.
Q.11 What is the position of H with respect to E?
- Immediate left
- Second to the left
- Third to the left
- Third to the right
- None of these.
Answer: C
Solution 11: H is third to the left of F
Q.12 Which of the following pairs represents the people standing at the extreme ends of the line?
- G, I
- D, F
- E, F
- D, I
- None of these
Answer: B
Solution 12: D and F are sitting at the extreme ends
Q.13 Who is standing second to the right of D?
- G
- E
- H
- F
- None of these
Answer: C
Solution 13: H is standing second to the right of D
Q.14 Four of the following five are alike in a certain way based on their positions in the above arrangement and so form a group. Which of the following does not belong to that group?
- D, H
- H, F
- H, I
- E, F
- G, E
Answer: B
Solution 14: In all the options except ‘H, F’, there is only one person standing between the both
Q. 15 If all the persons are asked to stand in alphabetical order from left to right, the positions of how many will remain unchanged?
- One
- Two
- Three
- None
- None of these
Answer: A
Solution 15: The positions of people after rearranging them in alphabetical order from left to right are; therefore, the position of only one, thus D remains unchanged.
Directions (Q.16 – Q.18): Read the following information carefully to answer the question below:
If B + C means B is the father of C
If B x C means B is the sister of C
If B $ C means B is the wife of C
If B % C means B is the mother of C
If B ÷ C mans B is the son of C
Q.16 What should come in place of the question mark to establish that K is the brother of U in the expression?
K ÷ Q % I ? U % M
- X
- ÷
- $
- Either ÷ or X
- Either + or ÷
Answer: A
Solution 16: K is brother of U
Q.17 Which among the given expressions indicates that N is the daughter of E?
- M % S $ E + U x N
- M + S $ E + N x U
- L % S % E + U ÷ N
- E + M $ S + N x U
- M $ E ÷ S % N ÷ U
Answer: B
Solution 17: N is the daughter of E
Q.18 Which among the following options is true if the expression ‘J + U % K x M ÷ L’ is definitely true?
- M is the daughter of U
- L is the son-in-law of J
- J is the grandmother of M
- U is the father K
- K is the brother of M
Answer: B
Solution 18: L is the son-in-law of J
Directions (Q.19 – Q.22): Choose the word/ phrase that is most similar in meaning to the word printed in bold as used in the passage.
Q.19 Starved
- Deprived
- Disadvantaged
- Hungry
- Fasting
- Emaciated
Answer: C
Solution 19: ‘Starved’ is used for resources and investment. So, it means being deprived
Q.20 Slapped
- Beaten
- Imposed
- Withdrawn
- Avoided
- Persuaded
Answer: B
Solution 20: When something is said to be slapped’ on someone or something, the word ‘slap’ refers to imposition
Q.21 Plowed
- Cultivated
- Bulldozed
- Recovered
- Instilled
- Withdrew
Answer: A
Solution 21: ‘Plowed’ or ‘ploughed’ means to cultivate
Q.22 Crestfallen
- Despair
- Cheerful
- Despondent
- Scatter
- Hairbrain
Answer: C
Solution 22: Despondent means to be unhappy
Directions Q.23 – Q.25: Read each sentence to find out whether there are any kind of grammatical error(s) in them. The error, if any will be in any part of the sentence. The number designated to that part will be the error. If there is no error, the answer is (5). You can ignore any errors in punctuation in the event of any that are found.
Q.23 The biggest (A) / health burden that India (B)/ is set to face in the coming years (C) / is tackle cancer. (D) / No error (E)
Answer: D
Solution 23: Here, infinitive i.e. is to tackle cancer….. Should be used
Q.24 Illegal sand mining in the peripheral areas (A) / of the district continues to remain a big problem for (B) / forest range officers as yet another instance illegal (C) / mining was reported yesterday. (D) / No error (E)
Answer: C
Solution 24: Here, forest range officers as yet another instance of illegal ….. Should be used
Q.25 The policemen, who (A) / was deployed heavily (B) / in the area did nothing to (C) / dissuade the protestors. (D) / No error (E)
Answer: B
Solution 25: Here, subject (The policemen) is plural. Hence, plural verb i.e. were deployed heavily… should be used.
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