Number System

JKSSB Assistant Training Officer (Handicrafts & Handlooms) · Numerical Ability · 99 practice questions with answers and explanations: 45 Easy, 49 Medium, 5 Hard.

Sample questions

Sample Easy question 1

Which of the following is a composite number: 23, 29, 33, 37?

  1. 33
  2. 29
  3. 23
  4. 37
Show answer

Answer: A. 33 = 3×11 is composite; the others are prime.

Sample Easy question 2

Which of the following is a composite number: 41, 43, 45, 47?

  1. 43
  2. 47
  3. 41
  4. 45
Show answer

Answer: D. 45 = 9×5 is composite; the others are prime.

Sample Easy question 3

Find the smallest 3-digit number divisible by 7.

  1. 100
  2. 104
  3. 102
  4. 105
Show answer

Answer: D. 100/7 ≈ 14.3, so the next multiple, 15×7 = 105, is the smallest 3-digit multiple.

Sample Medium question 4

Find the remainder when 2¹⁰⁰ is divided by 7.

  1. 1
  2. 2
  3. 4
  4. 6
Show answer

Answer: B. Powers of 2 mod 7 cycle as 2,4,1 (period 3); 100 mod 3 = 1, giving remainder 2.

Sample Medium question 5

Find the unit digit of 7¹²³.

  1. 7
  2. 1
  3. 9
  4. 3
Show answer

Answer: D. Unit digits of powers of 7 cycle as 7,9,3,1 (period 4); 123 mod 4 = 3, giving unit digit 3.

Sample Medium question 6

Find the unit digit of 13¹⁰¹.

  1. 7
  2. 9
  3. 3
  4. 1
Show answer

Answer: C. Unit digit follows powers of 3, which cycle as 3,9,7,1 (period 4); 101 mod 4 = 1, giving unit digit 3.

Sample Hard question 7

Find the number of digits in 5¹⁵ (use log₁₀5 ≈ 0.69897).

  1. 12
  2. 10
  3. 9
  4. 11
Show answer

Answer: D. 15 × 0.69897 ≈ 10.48; number of digits = ⌊10.48⌋ + 1 = 11.

Sample Hard question 8

Find the remainder when 23²³ is divided by 24.

  1. 19
  2. 1
  3. 23
  4. 11
Show answer

Answer: C. 23 ≡ -1 (mod 24); (-1)²³ = -1 ≡ 23 (mod 24).

Sample Hard question 9

Find the remainder when 3¹⁰⁰ is divided by 7.

  1. 4
  2. 6
  3. 1
  4. 2
Show answer

Answer: A. Powers of 3 mod 7 cycle as 3,2,6,4,5,1 (period 6); 100 mod 6 = 4, giving remainder 4.

More Numerical Ability topics for JKSSB Assistant Training Officer (Handicrafts & Handlooms)

Related articles