Number System

LSSSSB Non-Technical · Mathematics · 99 practice questions with answers and explanations: 45 Easy, 49 Medium, 5 Hard.

Sample questions

Sample Easy question 1

What is the place value of 7 in 4,753?

  1. 7000
  2. 70
  3. 7
  4. 700
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Answer: D. The digit 7 is in the hundreds place, so its place value is 700.

Sample Easy question 2

What is the place value of 5 in 58,231?

  1. 5
  2. 500
  3. 50000
  4. 5000
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Answer: C. The digit 5 is in the ten-thousands place, so its place value is 50,000.

Sample Easy question 3

Is 111 divisible by 3?

  1. Yes
  2. No
  3. Only by 9, not 3
  4. Cannot be determined
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Answer: A. The digit sum of 111 is 3, which is divisible by 3, so 111 is divisible by 3.

Sample Medium question 4

Find the unit digit of 127³².

  1. 3
  2. 1
  3. 7
  4. 9
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Answer: B. Unit digit follows powers of 7, which cycle as 7,9,3,1 (period 4); 32 mod 4 = 0, giving unit digit 1.

Sample Medium question 5

How many two-digit numbers are divisible by 9?

  1. 8
  2. 9
  3. 10
  4. 11
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Answer: C. Two-digit multiples of 9 run from 18 to 99: (99-18)/9 + 1 = 10.

Sample Medium question 6

How many two-digit numbers are divisible by 4?

  1. 20
  2. 23
  3. 22
  4. 21
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Answer: C. Two-digit multiples of 4 run from 12 to 96: (96-12)/4 + 1 = 22.

Sample Hard question 7

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.

Sample Hard question 8

Find the number of digits in 2³⁰ (use log₁₀2 ≈ 0.30103).

  1. 11
  2. 9
  3. 8
  4. 10
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Answer: D. 30 × 0.30103 ≈ 9.03; number of digits = ⌊9.03⌋ + 1 = 10.

Sample Hard question 9

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.

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