**Quantitative Aptitude Practice questions on Number System- Remainders**: This practice set has 10 questions with their answers & Explanatory answer covering topics from the areas of Quantitative Aptitude.

**1. The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?**

A. 7

B. 29

C. 16

D. 13

**2.** **What is the remainder when (13 ^{100} + 17^{100}) is divided by 25?**

A. 0

B. 2

C. 4

D. 11

**3. A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?**

A. 2

B. 0

C. 1

D. 3

**4.** **N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?**

A. 3

B. 5

C. 4

D. 2

**5.** **What is the remainder when we divide 3 ^{90} + 5^{90} by 34?**

A. 0

B. 17

C. 33

D. 1

**6.** **N ^{2} leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?**

A. 1, 5, 7 and 11

B. 1 and 5

C. 5, 9, and 11

D. 1 and 11

**7.** **A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?**

A. 8

B. 12

C. 9

D. 15

**8.** **How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?**

A. 32

B. 36

C. 24

D. 19

**9.** **Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?**

A. 65

B. 96

C. 125

D. More than one value is possible

**10.** **A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?**

A. 3

B. 2

C. 5

D. 4

**Answer Key –**

Q.No. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. |
---|---|---|---|---|---|---|---|---|---|---|

Ans. | (B) | (B) | (A) | (B) | (A) | (A) | (B) | (B) | (D) | (C) |

**Solutions Link -** http://iim-cat-questions-answers.2iim.com/quant/number-system/remainders/