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XAT Number System Questions with Answers & Explanations

20 Number System questions from the Quantitative Ability & Data Interpretation section of XAT, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

What is the unit digit of 17^95?

  1. A0
  2. B3
  3. C7
  4. D8
  5. E4
Show answer
Answer: (B) 3 Unit digits of powers of 7 repeat in a cycle of 4; 95 mod 4 = 3, so the unit digit is 3.
Question 2

What is the square root of 5041?

  1. A70
  2. B72
  3. C71
  4. D73
  5. E68
Show answer
Answer: (C) 71 71 × 71 = 5041.
Question 3

What is the value of 50² − 39²?

  1. A979
  2. B990
  3. C1079
  4. D121
  5. E879
Show answer
Answer: (A) 979 a² − b² = (a + b)(a − b) = 89 × 11 = 979.
Question 4

What is the remainder when 11815 is divided by 17?

  1. A1
  2. B12
  3. C8
  4. D0
  5. E10
Show answer
Answer: (D) 0 11815 = 17 × 695 + 0.
Question 5

What is the sum of the first 58 natural numbers?

  1. A1653
  2. B1711
  3. C1769
  4. D3364
  5. ENone of these
Show answer
Answer: (B) 1711 Sum = n(n + 1)/2 = 58 × 59/2 = 1711.
Question 6

What is the unit digit of 7^70?

  1. A7
  2. B6
  3. C9
  4. D0
  5. E1
Show answer
Answer: (C) 9 Unit digits of powers of 7 repeat in a cycle of 4; 70 mod 4 = 2, so the unit digit is 9.
Question 7

What is the value of 75² − 40²?

  1. A4025
  2. B4125
  3. C4060
  4. D1225
  5. E3925
Show answer
Answer: (A) 4025 a² − b² = (a + b)(a − b) = 115 × 35 = 4025.
Question 8

What is the remainder when 60225 is divided by 7?

  1. A6
  2. B4
  3. C0
  4. D5
  5. E3
Show answer
Answer: (B) 4 60225 = 7 × 8603 + 4.
Question 9

What is the square root of 1764?

  1. A44
  2. B42
  3. C43
  4. D41
  5. E39
Show answer
Answer: (B) 42 42 × 42 = 1764.
Question 10

What is the sum of the first 93 natural numbers?

  1. A8649
  2. B4278
  3. C4371
  4. D4464
  5. ENone of these
Show answer
Answer: (C) 4371 Sum = n(n + 1)/2 = 93 × 94/2 = 4371.

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Question 11

What is the unit digit of 17^81?

  1. A9
  2. B4
  3. C7
  4. D6
  5. E3
Show answer
Answer: (C) 7 Unit digits of powers of 7 repeat in a cycle of 4; 81 mod 4 = 1, so the unit digit is 7.
Question 12

What is the value of 83² − 23²?

  1. A6360
  2. B6460
  3. C6420
  4. D3600
  5. E6260
Show answer
Answer: (A) 6360 a² − b² = (a + b)(a − b) = 106 × 60 = 6360.
Question 13

What is the remainder when 72377 is divided by 13?

  1. A1
  2. B2
  3. C6
  4. D4
  5. E3
Show answer
Answer: (C) 6 72377 = 13 × 5567 + 6.
Question 14

What is the square root of 9604?

  1. A97
  2. B98
  3. C100
  4. D95
  5. E99
Show answer
Answer: (B) 98 98 × 98 = 9604.
Question 15

What is the HCF of 36 and 60?

  1. A12
  2. B36
  3. C15
  4. D24
  5. E6
Show answer
Answer: (A) 12 36 = 12 × 3 and 60 = 12 × 5, so HCF = 12.
Question 16

What is the sum of the first 29 natural numbers?

  1. A841
  2. B435
  3. C464
  4. D406
  5. ENone of these
Show answer
Answer: (B) 435 Sum = n(n + 1)/2 = 29 × 30/2 = 435.
Question 17

What is the unit digit of 4^62?

  1. A8
  2. B4
  3. C3
  4. D7
  5. E6
Show answer
Answer: (E) 6 Unit digits of powers of 4 repeat in a cycle of 4; 62 mod 4 = 2, so the unit digit is 6.
Question 18

What is the value of 85² − 23²?

  1. A6696
  2. B3844
  3. C6596
  4. D6796
  5. E6758
Show answer
Answer: (A) 6696 a² − b² = (a + b)(a − b) = 108 × 62 = 6696.
Question 19

What is the remainder when 46527 is divided by 9?

  1. A3
  2. B8
  3. C6
  4. D4
  5. E2
Show answer
Answer: (C) 6 46527 = 9 × 5169 + 6.
Question 20

What is the square root of 225?

  1. A17
  2. B15
  3. C16
  4. D12
  5. E14
Show answer
Answer: (B) 15 15 × 15 = 225.

These are RankerClub practice questions written in the XAT pattern. They are not official SSC/IBPS/RRB papers.

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