SSC CGL Number System Practice Test 3

1. Which number is divisible by 11?

• A. 121 (Correct)
• B. 123
• C. 125
• D. 127

Explanation: 121 is divisible by 11 exactly.

2. How many factors does 64 have?

• A. 6
• B. 7 (Correct)
• C. 8
• D. 9

Explanation: 64 = 2^6, so number of factors = 6 + 1 = 7.

3. Which is a prime number?

• A. 57
• B. 59 (Correct)
• C. 63
• D. 69

Explanation: 59 has no divisors other than 1 and itself.

4. Remainder when 523 is divided by 8 is:

• A. 1
• B. 2
• C. 3 (Correct)
• D. 4

Explanation: 8 x 65 = 520, so remainder = 3.

5. LCM of 9 and 12 is:

• A. 18
• B. 24
• C. 36 (Correct)
• D. 72

Explanation: LCM of 9 and 12 is 36.

6. HCF of 56 and 72 is:

• A. 4
• B. 6
• C. 8 (Correct)
• D. 12

Explanation: 8 is the greatest common divisor of 56 and 72.

7. The unit digit of 2^9 is:

• A. 2 (Correct)
• B. 4
• C. 6
• D. 8

Explanation: Powers of 2 repeat 2, 4, 8, 6. 9 mod 4 = 1, so unit digit is 2.

8. Odd + odd is always:

• A. Even (Correct)
• B. Odd
• C. Prime
• D. Composite

Explanation: Sum of two odd numbers is always even.

9. If a number leaves remainder 3 when divided by 5, what remainder will its square leave when divided by 5?

• A. 1
• B. 2
• C. 3
• D. 4 (Correct)

Explanation: If n ≡ 3 (mod 5), then n^2 ≡ 9 ≡ 4 (mod 5).

10. A number divisible by 8 must have its last three digits divisible by:

• A. 2
• B. 4
• C. 8 (Correct)
• D. 16

Explanation: Divisibility by 8 depends on the last three digits.

11. Prime factorization of 90 is:

• A. 2 x 3^2 x 5 (Correct)
• B. 2^2 x 3 x 5
• C. 3^2 x 5^2
• D. 2 x 3 x 5^2

Explanation: 90 = 2 x 3 x 3 x 5.

12. The unit digit of 4^8 is:

• A. 2
• B. 4
• C. 6 (Correct)
• D. 8

Explanation: Powers of 4 alternate between 4 and 6; even powers end in 6.