Q1. What is the square of 28?
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Answer: D. 784
28² = 784.
Number System Questions for SSC CGL (with Answers)
47 Number System MCQs from the Quantitative Aptitude section, with answers and short explanations.
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Q2. What is the square of 13?
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Answer: C. 169
13² = 169.
Q3. What is the sum of the first 20 natural numbers?
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Answer: A. 210
Sum = 20 × 21/2 = 210.
Q4. What is the sum of the first 30 natural numbers?
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Answer: B. 465
Sum = 30 × 31/2 = 465.
Q5. What is the sum of the first 40 natural numbers?
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Answer: C. 820
Sum = 40 × 41/2 = 820.
Q6. What is the sum of the first 100 natural numbers?
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Answer: D. 5050
Sum = 100 × 101/2 = 5050.
Q7. What is the sum of the first 25 natural numbers?
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Answer: D. 325
Sum = 25 × 26/2 = 325.
Q8. What is the largest 3-digit number exactly divisible by 9?
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Answer: C. 999
999 ÷ 9 leaves remainder 0. 999 − 0 = 999.
Q9. What is the smallest 3-digit number exactly divisible by 13?
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Answer: C. 104
100 ÷ 13 leaves remainder 9. 100 + 4 = 104.
Q10. What is the smallest 4-digit number exactly divisible by 9?
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Answer: B. 1008
1000 ÷ 9 leaves remainder 1. 1000 + 8 = 1008.
Q11. What is the largest 3-digit number exactly divisible by 23?
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Answer: A. 989
999 ÷ 23 leaves remainder 10. 999 − 10 = 989.
Q12. What is the square of 45?
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Answer: A. 2025
45² = 2025.
Q13. What is the unit digit of 3^97?
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Answer: B. 3
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 97 leaves remainder 1 on division by 4, so take the 1st value in the cycle: 3.
Q14. What is the unit digit of 3^90?
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Answer: A. 9
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 90 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q15. What is the unit digit of 3^75?
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Answer: B. 7
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 75 leaves remainder 3 on division by 4, so take the 3rd value in the cycle: 7.
Q16. What is the unit digit of 17^114?
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Answer: A. 9
Unit digits of 7^1, ^2, ^3, ^4 are 7, 9, 3, 1. 114 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q17. What is the unit digit of 4^83?
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Answer: B. 4
Unit digits of 4^1, ^2, ^3, ^4 are 4, 6, 4, 6. 83 leaves remainder 3 on division by 4, so take the 3rd value in the cycle: 4.
Q18. What is the unit digit of 17^198?
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Answer: A. 9
Unit digits of 7^1, ^2, ^3, ^4 are 7, 9, 3, 1. 198 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q19. What is the unit digit of 7^152?
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Answer: C. 1
Unit digits of 7^1, ^2, ^3, ^4 are 7, 9, 3, 1. 152 leaves remainder 0 on division by 4, so take the 4th value in the cycle: 1.
Q20. How many factors (divisors) does 225 have?
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Answer: D. 9
225 = 3^2 × 5^2; number of factors = 3 × 3 = 9.
Q21. How many factors (divisors) does 144 have?
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Answer: B. 15
144 = 2^4 × 3^2; number of factors = 5 × 3 = 15.
Q22. What is the unit digit of 9^82?
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Answer: D. 1
Unit digits of 9^1, ^2, ^3, ^4 are 9, 1, 9, 1. 82 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 1.
Q23. What is the largest 4-digit number exactly divisible by 29?
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Answer: D. 9976
9999 ÷ 29 leaves remainder 23. 9999 − 23 = 9976.
Q24. What is the largest 3-digit number exactly divisible by 13?
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Answer: B. 988
999 ÷ 13 leaves remainder 11. 999 − 11 = 988.
Q25. How many factors (divisors) does 72 have?
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Answer: D. 12
72 = 2^3 × 3^2; number of factors = 4 × 3 = 12.
Q26. What is the unit digit of 3^38?
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Answer: D. 9
Unit digits of 3^1, ^2, ^3, ^4 are 3, 9, 7, 1. 38 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 9.
Q27. How many factors (divisors) does 360 have?
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Answer: B. 24
360 = 2^3 × 3^2 × 5; number of factors = 4 × 3 × 2 = 24.
Q28. What is the smallest 4-digit number exactly divisible by 19?
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Answer: D. 1007
1000 ÷ 19 leaves remainder 12. 1000 + 7 = 1007.
Q29. What is the largest 4-digit number exactly divisible by 19?
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Answer: C. 9994
9999 ÷ 19 leaves remainder 5. 9999 − 5 = 9994.
Q30. How many factors (divisors) does 252 have?
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Answer: C. 18
252 = 2^2 × 3^2 × 7; number of factors = 3 × 3 × 2 = 18.
Q31. How many factors (divisors) does 120 have?
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Answer: A. 16
120 = 2^3 × 3 × 5; number of factors = 4 × 2 × 2 = 16.
Q32. What is the unit digit of 8^121?
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Answer: C. 8
Unit digits of 8^1, ^2, ^3, ^4 are 8, 4, 2, 6. 121 leaves remainder 1 on division by 4, so take the 1st value in the cycle: 8.
Q33. What is the smallest 4-digit number exactly divisible by 37?
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Answer: B. 1036
1000 ÷ 37 leaves remainder 1. 1000 + 36 = 1036.
Q34. What is the square of 65?
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Answer: D. 4225
65² = 4225.
Q35. What is the square of 67?
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Answer: A. 4489
67² = 4489.
Q36. What is the remainder when 7792 is divided by 11?
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Answer: C. 4
7792 = 11 × 708 + 4. Remainder = 4.
Q37. What is the remainder when 9806 is divided by 13?
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Answer: A. 4
9806 = 13 × 754 + 4. Remainder = 4.
Q38. What is the remainder when 1549 is divided by 7?
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Answer: A. 2
1549 = 7 × 221 + 2. Remainder = 2.
Q39. What is the remainder when 1103 is divided by 9?
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Answer: B. 5
1103 = 9 × 122 + 5. Remainder = 5.
Q40. What is the remainder when 9792 is divided by 11?
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Answer: C. 2
9792 = 11 × 890 + 2. Remainder = 2.
Q41. What is the remainder when 7474 is divided by 13?
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Answer: B. 12
7474 = 13 × 574 + 12. Remainder = 12.
Q42. What is the remainder when 6647 is divided by 13?
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Answer: B. 4
6647 = 13 × 511 + 4. Remainder = 4.
Q43. How many factors (divisors) does 24 have?
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Answer: A. 8
24 = 2^3 × 3; number of factors = 4 × 2 = 8.
Q44. What is the remainder when 9026 is divided by 11?
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Answer: D. 6
9026 = 11 × 820 + 6. Remainder = 6.
Q45. How many factors (divisors) does 196 have?
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Answer: B. 9
196 = 2^2 × 7^2; number of factors = 3 × 3 = 9.
Q46. What is the remainder when 5038 is divided by 11?
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Answer: C. 0
5038 = 11 × 458 + 0. Remainder = 0.
Q47. How many factors (divisors) does 200 have?
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Answer: D. 12
200 = 2^3 × 5^2; number of factors = 4 × 3 = 12.
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