## Divisibility questions for SSC: Number system questions with answers

Solve 10 divisibility questions for SSC in number system for SSC CGL Set 46 in 12 mins. Verify from answers. Learn to solve from solutions.

Majority of the 10 questions are on divisibility, division and Euler's division lemma.

Answers and link to the solution set are at the end.

### 10 divisibility questions for SSC and other number system questions in SSC CGL Set 46 - time to answer 12 mins

**Problem 1.**

Two numbers 7655 and 11284 when divided by a third number of three digits, the remainder left in both cases is same. The sum of the digits of the three digit number is then,

- 9
- 11
- 10
- 8

**Problem 2.**

The value of $(0.34\overline{68}+0.17\overline{32})$ is,

- $0.52\overline{01}$
- $0.\overline{51}$
- $0.52$
- $0.5\overline{1}$

**Problem 3.**

If $p$ and $q$ are positive integers and $(p-q)$ is an even number, then $(p^2-q^2)$ will always be divisible by,

- 4
- 6
- 12
- 8

**Problem 4.**

3957 is added to 5349 and 7062 is subtracted from the resulting sum. The final result is then not divisible by,

- 3
- 4
- 7
- 11

**Problem 5.**

If the sum of digits of any integer lying between 100 and 1000 is subtracted from the number, the result will always be divisible by,

- 9
- 6
- 2
- 5

#### Problem 6.

How many numbers between 400 and 900 are divisible by 4, 5 and 6?

- 8
- 7
- 9
- 10

** Problem 7.**

When a number is divided by 56, the remainder left is 29. What will be the remainder when the number is divided by 7?

- 6
- 3
- 1
- 2

** Problem 8.**

64329 is divided by a certain number getting 175, 114 and 213 as three successive remainders. The divisor is then,

- 296
- 234
- 184
- 224

**Problem 9.**

A number when successively divided by 4 and 5 leaves remainders 1 and 4 respectively. The remainders left when the number is divided by 5 and 4 successively will be,

- 1, 4
- 2, 1
- 2, 3
- 3, 2

** Problem 10.**

If two numbers are each divided by the same number the remainders are respectively 4 and 3. If again the sum of the numbers are divided by the same divisor, the remainder now is 2. The divisor is,

- 3
- 9
- 5
- 7

Learn to solve the questions quickly from the paired solution set at,

**SSC CGL Solution set 46 on Number system and Divisibility questions.**

### Answers to the divisibility questions for SSC and other number system questions in SSC CGL Set 46

**Problem 1. Answer:** b: 11.

**Problem 2.** **Answer:** Option a : $0.52\overline{01}$ .

**Problem 3. Answer:** Option a: 4.

**Problem 4.** **Answer:** c: 7.

**Problem 5.** **Answer:** Option a: 9.

**Problem 6.** **Answer:** Option a : 8.

**Problem 7.** **Answer:** Option c: 1.

**Problem 8.** **Answer:** Option b: 234.

**Problem 9.** **Answer:** Option c: 2, 3.

**Problem 10.** **Answer:** Option c: 5.

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