Number System

Ladakh Police Constable · Mathematics · 99 practice questions with answers and explanations: 45 Easy, 49 Medium, 5 Hard.

Sample questions

Sample Easy question 1

Find the HCF of 24 and 36.

  1. 6
  2. 18
  3. 8
  4. 12
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Answer: D. The highest common factor of 24 and 36 is 12.

Sample Easy question 2

Find the LCM of 8 and 12.

  1. 32
  2. 24
  3. 16
  4. 20
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Answer: B. The least common multiple of 8 and 12 is 24.

Sample Easy question 3

If a number is divisible by both 9 and 11, it must also be divisible by:

  1. 88
  2. 110
  3. 99
  4. 90
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Answer: C. Since 9 and 11 are coprime, their LCM is 99, and any number divisible by both must be divisible by 99.

Sample Medium question 4

How many multiples of 6 are there between 1 and 300?

  1. 52
  2. 45
  3. 48
  4. 50
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Answer: D. 300/6 = 50.

Sample Medium question 5

How many multiples of 8 are there between 1 and 400?

  1. 50
  2. 48
  3. 52
  4. 45
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Answer: A. 400/8 = 50.

Sample Medium question 6

The HCF and LCM of two numbers are 12 and 360. If one number is 72, find the other.

  1. 57
  2. 63
  3. 60
  4. 54
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Answer: C. Product of numbers = HCF × LCM = 12 × 360 = 4320; other number = 4320/72 = 60.

Sample Hard question 7

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

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

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