Number System

J&K Bank Banking Associate · Quantitative Aptitude · 99 practice questions with answers and explanations: 45 Easy, 49 Medium, 5 Hard.

Sample questions

Sample Easy question 1

The product of two numbers is 3600 and their HCF is 20. Find their LCM.

  1. 174
  2. 183
  3. 180
  4. 177
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Answer: C. LCM = 3600/20 = 180.

Sample Easy question 2

A number when divided by 7 gives a quotient of 12 and a remainder of 5. Find the number.

  1. 86
  2. 83
  3. 89
  4. 92
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Answer: C. Number = divisor × quotient + remainder = 7×12 + 5 = 89.

Sample Easy question 3

A number when divided by 9 gives a quotient of 15 and a remainder of 4. Find the number.

  1. 139
  2. 133
  3. 142
  4. 136
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Answer: A. Number = 9×15 + 4 = 139.

Sample Medium question 4

Find the remainder when 2¹⁰ is divided by 7.

  1. 2
  2. 3
  3. 1
  4. 4
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Answer: A. 2¹⁰ = 1024 = 146×7 + 2, so the remainder is 2.

Sample Medium question 5

How many two-digit numbers are divisible by 7?

  1. 14
  2. 11
  3. 12
  4. 13
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Answer: D. The two-digit multiples of 7 run from 14 to 98: (98-14)/7 + 1 = 13.

Sample Medium question 6

Find the unit digit of 7⁴⁵.

  1. 1
  2. 7
  3. 3
  4. 9
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Answer: B. The unit digits of powers of 7 cycle as 7,9,3,1 with period 4; 45 mod 4 = 1, so the unit digit is 7.

Sample Hard question 7

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 8

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 9

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.

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