Number System

JKSSB Junior Engineer (Mechanical) · Mathematics · 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: 41, 43, 45, 47?

  1. 43
  2. 47
  3. 41
  4. 45
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Answer: D. 45 = 9×5 is composite; the others are prime.

Sample Easy question 2

Find the smallest 3-digit number divisible by 7.

  1. 100
  2. 104
  3. 102
  4. 105
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Answer: D. 100/7 ≈ 14.3, so the next multiple, 15×7 = 105, is the smallest 3-digit multiple.

Sample Easy question 3

Find the smallest 3-digit number divisible by 9.

  1. 103
  2. 108
  3. 106
  4. 105
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Answer: B. 100/9 ≈ 11.1, so the next multiple, 12×9 = 108, is the smallest 3-digit multiple.

Sample Medium question 4

Find the largest number that divides 62 and 100, leaving a remainder of 2 in each case.

  1. 2
  2. 8
  3. 4
  4. 6
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Answer: A. The required number is HCF(60, 98) = 2.

Sample Medium question 5

Find the smallest number which, when divided by 8, 12 and 16, leaves a remainder of 5 in each case.

  1. 56
  2. 48
  3. 51
  4. 53
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Answer: D. LCM(8,12,16) = 48; the required number = 48 + 5 = 53.

Sample Medium question 6

Find the smallest number which, when divided by 6, 9 and 12, leaves a remainder of 4 in each case.

  1. 38
  2. 36
  3. 42
  4. 40
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Answer: D. LCM(6,9,12) = 36; the required number = 36 + 4 = 40.

Sample Hard question 7

Find the remainder when 23²³ is divided by 24.

  1. 19
  2. 1
  3. 23
  4. 11
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Answer: C. 23 ≡ -1 (mod 24); (-1)²³ = -1 ≡ 23 (mod 24).

Sample Hard question 8

Find the remainder when 3¹⁰⁰ is divided by 7.

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

Sample Hard question 9

Find the remainder when 1³ + 2³ + ... + 10³ is divided by 9.

  1. 3
  2. 0
  3. 1
  4. 2
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Answer: C. Sum of cubes 1 to 10 is 3025; 3025 mod 9 = 1.

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