Find the correct answer for each of the following:
Q1: The smallest whole number is
(a) 1 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 0 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(b) 0
The smallest whole number is 0.
Q2: The least number of 4 digit which is exactly divisible by 9 is
(a) 1018 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 1026 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 1009 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 1008
Sol:
(d) 1008
(a)
Hence, 1018 is not exactly divisible by 9.
(b)
Here, 1026 is exactly divisible by 9.
(c)
Here, 1008 is not exactly divisible by 9.
(d)
Hence, 1008 is exactly divisible by 9.
(b) and (d) are exactly divisible by 9, but (d) is the least number which is exactly divisible by 9.
Q3: The largest number of 6 digits which is exactly divisible by 16 is
(a) 999980 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 999982 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 999984 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 999964
Sol:
(c) 999984
(a)
Hence, 999980 is not exactly divisible by 16.
(b)
Hence, 999982 is not exactly divisible by 16.
(c)
Hence, 999984 is exactly divisible by 16.
Hence, 999964 is not exactly divisible by 16.
The largest six digit number which is exactly divisible by 16 is 999984.
Q4: What least number should be subtracted from 10004 to get a number exactly divisible by 12?
(a) 4 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 6 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 8 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 20
Sol:
(c) 8
Here we have to tell what least number should be subtracted from 1004 to get a number exactly divisible by 12.
So, we will first divide 1004 by 12.
Remainder = 8
So, 8 should be subtracted from 1004 to get the number exactly divisible by 12.
i.e. 1004 – 8 = 9996
Hence, 9996 is exactly divisible by 12.
Q5: What least number should be added to 10056 to get a number exactly divisible by 23?
(a) 5 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 18 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 13 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 10
Sol:
(a) 18
Here, we have to tell what least number must be added to 1056 to get a number exactly divisible by 23.
So, first we will divide 1056 by 23.
Remainder = 5
Required number = 23 – 5 = 18
So, 18 must be added to 1056 to get a number exactly divisible by 23.
Hence, 10074 is exactly divisible by 23.
Q6: What least number is nearest to 457 which is divisible by 11?
(a) 450 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 451 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 460 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 462
Sol:
(d) 462
(a)
Hence, 450 is not divisible by 11.
(b)
Hence, 451 is divisible by 11.
(c)
Hence, 460 is not divisible by 11.
(d)
Hence, 462 is divisible by 11.
Here, the number given in the options (b) and (d) are divisible by 11. However, we want a whole number nearest to 457 which is divisible by 11.
So, 462 is whole number nearest to 457 and divisible by 11.
Q7: How many whole numbers are there between 1018 and 1203?
(a) 185 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 186 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 184 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(c) 184
Number of whole numbers = (1203 – 1018) – 1
= 185 – 1
= 184
Q8 : A number when divided by 46 gives 11 as quotient and 15 as remainder. The number is
(a) 491 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 521 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 701 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 679
Sol:
(b) 521
Divisor = 46
Quotient = 11
Remainder = 15
Dividend = Divisor \(\times\) quotient + remainder
= 46 \(\times\) 11 + 15
= 506 + 15
= 521
Q9: In a division sum, we have dividend = 199, quotient = 16 and remainder = 7. The divisor is
(a) 11 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 23 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 12 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(c) 12
Dividend = 199
Quotient = 16
Remainder = 7
According to the division algorithm, we have:
Dividend = Divisor \(\times\) quotient + remainder
\(\Rightarrow \) 199 = Divisor \( \times \) 16 + 7
\(\Rightarrow \) 199 – 7 = Divisor \( \times \) 16
\(\Rightarrow \) Divisor = 192 \(\div\) 16
Q10: 7589 – ? = 3434
(a) 11023 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 4245 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 4155 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(a) 11023
7589 – ? = 3434
\(\Rightarrow\) 7589 – x = 3434
\(\Rightarrow\) x = 7589 + 3434
\(\Rightarrow\) x = 11023
Q11: 587 \(\times\) 99 = ?
(a) 57213 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 58513 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 58113 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 56413
Sol:
(c) 58113
587 \(\times\) 99
= 587 \(\times\) (100 – 1)
= 587 \(\times\) 100 – 587 \(\times\) 1
= 58700 – 587
= 58113
Q12: Â 4 \(\times\) 538 \(\times\) 25 = ?
(a) 32280 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 26900 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 53800 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 10760
Sol:
(c) 53800
4 \(\times\) 538 \(\times\) 25
= 100 \(\times\) 538
= 53800
Q13: 24679 \(\times\) 92 + 24679 \(\times\) 8 = ?
(a) 493580 Â Â Â Â Â Â Â Â Â Â Â (b) 1233950 Â Â Â Â Â Â Â Â Â Â Â (c) 2467900 Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(c) 2467900
By using the distributive property, we have:
24679 \(\times\) 92 + 24679 \(\times\) 8
= 24679 \(\times\) (92 + 8)
= 24679 \(\times\) 100
= 2467900
Q14: 1625 \(\times\) 1625 – 1625 \(\times\) 625
(a) 1625000 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 162500 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 325000 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 812500
Sol:
(a) 1625000
By using the distributive property, we have:
1625 \(\times\) 1625 – 1625 \(\times\) 625
= 1625 \(\times\) (1625 – 625)
= 1625 \(\times\) 1000
= 1625000
Q15: 1568 \(\times\) 185 – 1568 \(\times\) 85 = ?
(a) 7840 Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 15680 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 156800 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(c) 156800
By using the distributive property, we have;
1568 \(\times\) 185 – 1568 \(\times\) 85
= 1568 \(\times\) (185 – 85)
= 1568 \(\times\) 100
= 156800
Q16: (888 + 777 + 555) = (111 \(\times\) ?)
(a) 120 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 280 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 20 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) 140
Sol:
(c) 20
(888 + 777 + 555) = (111 \(\times\) ?)
\(\Rightarrow\) (888 + 777 + 555) = 111 \(\times\) (8 + 7 + 5) Â Â Â Â Â [by taking 111 common]
= 111 \(\times\) 20 = 2220
Q17: The sum of two odd numbers is
(a) an odd number  (b) an even number  (c) a prime number  (d) a multiple of 3
Sol:
(b) An even number
The sum of two odd numbers is an even number.
Example: 5 + 3 = 8
Q18:The product of two odd numbers is
(a) an odd number  (b) an even number  (c) a prime number  (d) none of these
Sol:
(a) an odd number
The product of two odd numbers is an odd number.
Example: 5 \(\times\) 3 = 15
Q19: If a is a whole number such that a + a = a, then a = ?
(a) 1 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) 3 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (d) none of these
Sol:
(d) None of these
Given: a is a whole number such that a + a = a
If a = 1, then 1 + 1 = 2 \(\neq\) 1
If a = 2, then 2 + 2 = 4 \(\neq\) 1
If a = 3, then 3 + 3 = 6 \(\neq\) 1
Q20: The predecessor of 10000 is
(a) 10001 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 9999 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) none of these
Sol:
(b) 9999
Predecessor of 10000 = 10000 – 1 = 9999
Q21: The successor of 1001 is
(a) 1000 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 1002 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) none of these
Sol:
(b) 1002
Successor of 1001 = 1001 + 1 = 1002
Q22: The smallest even whole number is
(a) 0 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (b) 2 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (c) none of these
Sol:
(b) 2
The smallest even whole number is 2. Zero is neither an even number nor an odd number.
