**SSC CGL Questions on Remainder**

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**Question 1: **A number, when divided by 114, leaves remainder 21. If the same number is divided by 19, then the remainder will be

a) 1

b) 2

c) 7

d) 17

**Question 2: **A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, the remainder will be

a) 9

b) 7

c) 3

d) 2

**Question 3: **A positive integer when divided by 425 gives a remainder 45. When the same number is divided by 17, the remainder will be

a) 11

b) 8

c) 9

d) 10

**Question 4: **When $2^{33}$ is divided by 10, the remainder will be

a) 2

b) 3

c) 4

d) 8

**Question 5: **A positive integer when divided by 425 gives a remainder 45. When the same number is divided by 17, the remainder will be

a) 11

b) 8

c) 9

d) 10

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**Question 6: **When a number is divided by 56, the remainder will be 29. If the same number is divided by 8, then the remainder will be

a) 6

b) 7

c) 5

d) 3

**Question 7: **If a perfect square, not divisible by 6, be divided by 6, the remainder will be

a) 1, 3 or 5

b) 1, 2 or 5

c) 1, 3 or 4

d) 1, 2 or 4

**Question 8: **A number, when divided by 296, gives 75 as the remainder. Ifthesamenumberis divided by 37 then the remainder will be

a) 1

b) 2

c) 19

d) 31

**Question 9: **The sum of the digits of a two-digit number is $\frac{1}{7}$ of the number. The units digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7, the remainder will be:

a) 4

b) 5

c) 1

d) 6

**Question 10: **A number is divided by 52, we get 27 as remainder. On dividing the same number by 13, What will be the remainder?

a) 2

b) 7

c) 1

d) None of these

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**Answers & Solutions:**

**1) Answer (B)**

Let the given number be *x*

Let a be the quotient when *x* is divided by 114

So $\frac{x}{114}$ = a$\frac{21}{114}$

so *x* = 114a + 21

when *x* is divided by 19 it can be written as

$\frac{x}{19} = \frac{114a + 21}{19}$

114 is divisible by 19 and 21 leaves a remainder of 2.

**2) Answer (D)**

Number will be (136n + 36) where n is quotient

hence when it is divided by 17 remainder for $\frac{136n +36}{17}$ will be 2 as 136 is divisible by 17 and 36=34+2

**3) Answer (A)**

Let the number be 45.

So, when 45 is divided by 425, the remainder is 45 and quotient is 0.

Now, when 45 is divided by 17, we get

quotient = 2

remainder = **11**

**4) Answer (A)**

$\frac{2^{33}}{10}$ = > $\frac{8^{11}}{10}$ => $\frac{-2^{11}}{10}$

= > $\frac{1024 \times -2}{10}$

= > $\frac{12}{10}$ –> remainder 2

**5) Answer (A)**

Let the number be 45

So, when 45 is divided by 425 => remainder = 45

Now, when 45 is divided by 17

=> Remainder = 45%17 = 11

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**6) Answer (C)**

When the number is divided by 56, remainder is 29

=> Let the number = 56+29 = 85

Now, if 85 is divided by 8, => $85=8\times 10+5$

Thus, remainder = 5

=> Ans – (C)

**7) Answer (C)**

**8) Answer (A)**

**9) Answer (D)**

**10) Answer (C)**

When a number is divided by 52, remainder obtained is 27,

=> Number is of the form = $52k+27$

When above number is divided by 13, => $\frac{(52k+27)}{13}$

$\because$ 52 is a multiple of 13, => $27\%13=1$

=> Ans – (C)

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