When preparing for placement exams, one of the most scoring yet tricky topics is the Number System. It is a foundation of quantitative aptitude and regularly appears in exams conducted by Infosys, TCS, Wipro, Accenture, Cognizant, LTI Mindtree, Capgemini, and even government exams.

To help you master this area, we have compiled a complete PYQ (Previous Year Questions) set from the Number System – Day 01 and Day 02 series. These 50+ questions cover every important concept tested in real exams.

Why Focus on Number System?

  • Weightage in exams: Almost every company includes 2–3 direct number system questions.

  • Conceptual base: Topics like factors, divisibility, factorial zeros, and remainders build the logic for tougher aptitude.

  • High-scoring: With proper practice, these questions can be solved in less than a minute.

Number System Day 01 – PYQ Set

Q1. If 3/4 of the difference of 2 1/4 and 1 2/3 is subtracted from 2/3 of 3 1/4, the result is
a) -48/83
b) 48/83
c) -83/48
d) 83/48
Answer: d) 83/48

Q2. P is the product of all prime numbers from 1 to 100. Then the number of zeros at the end of the product is
a) 0
b) 1
c) 24
d) None of these
Answer: b) 1

Q3. What is the highest power of 2 in 1! + 2! + 3! + … + 100!?
a) 24
b) 3
c) 0
d) 97
Answer: c) 0

Q4. If n = 1 + x, where x is the product of four consecutive positive integers, then which of the following is true?

  1. n is odd

  2. n is prime

  3. n is a perfect square
    a) 1 only
    b) 2 only
    c) 3 only
    d) 1 & 3 only
    Answer: d) 1 & 3 only

Q5. What is the maximum value of m if
N = 35 × 45 × 55 × 60 × 124 × 75
is divisible by 5^m ?
a) 4
b) 5
c) 6
d) 7
Answer: c) 6

Q6. The product of two consecutive even numbers is 9408. Which of the following is the greater number?
a) 96
b) 94
c) 92
d) 90
e) None of these
Answer: e) None of these (correct number is 98)

Q7. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the number?
a) 69
b) 78
c) 96
d) Cannot be determined
e) None of these
Answer: d) Cannot be determined (both 69 and 96 satisfy conditions)

Q8. Find the maximum number of trees which can be planted 10m apart on two sides of a straight road 1860m long.
Answer: 373

Q9. A man engaged a servant for Rs. 90 + a turban for one year. He served 9 months and received Rs. 65 + turban. Find the price of the turban.
Answer: Rs. 20

Q10. In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If remainder = 48, find the dividend.
a) 5808
b) 5809
c) 5484
d) 3472
Answer: a) 5808

Q11. If x and y are positive integers, is y odd?

  1. x is odd.

  2. xy is odd.
    Answer: Statement 2 alone is sufficient.

Q12. Is b^ab + b^(b+1) even? (a, b positive integers)

  1. b is even

  2. a is even
    Answer: Statement 1 alone is sufficient.

Q13. How many keystrokes are needed to type numbers from 1 to 1000?
a) 2704
b) 2890
c) 2893
d) 3001
Answer: c) 2893

Day 02: Number System PYQ

Q1. How many divisors of 1020?
a) 12
b) 20
c) 24
d) 36
Answer: c) 24

How many divisors of 1200?
a) 12
b) 30
c) 24
d) 36
Answer: b) 30

Q2. For N = 420, find:

  • Total number of factors

  • Number of even factors

  • Number of odd factors
    Answer: 24 total, 16 even, 8 odd

Q3. Find total number of factors of 888888.
Answer: 120

Q4. Find number of divisors of 50.
Answer: 6

Q5. Find trailing zeros in 25!.
Answer: 6

Q6. Division sum (same as Day01 Q13).
Answer: 5808

Q7. Least value of * in 451*603 divisible by 9?
Answer: 7

Q8. If 5432*7 divisible by 9, * = ?
Answer: 6

Q9. When 335 is added to 5A7, the result is 8B2 (divisible by 3). Find largest & smallest A.
Answer: Largest A = 9, Smallest A = 0

Q10. Find k in 9314k8025 divisible by 11.
Answer: 7

Q11. If 259876P05 divisible by 11, find (P^2 + 5).
Answer: 56

Q12. Which is divisible by 15?
Options: 2365, 1375, 4365, 2275
Answer: 1375

Q13. Which is NOT divisible by 18?
Options: 54036, 50436, 34056, 65043
Answer: 65043

Q14. Which is divisible by 24?
Options: 35718, 63810, 537804, 3125736
Answer: 3125736

Q15. Least 5-digit number divisible by 52, 56, 78, 91?
Answer: 10920

Q16. Greatest 6-digit number leaving remainder 10 when divided by 36, 48, 54, 60, 90?
Answer: 997910

Q17. Largest 4-digit number divisible by 88?
Answer: 9944

Q18. If 5432y1749x divisible by 72, find (5x – 4y).
Answer: 18

Q19. N = 897324P64Q divisible by 8 and 9. Value of P + Q?
Answer: 9

Q20. How many pairs (A,B) possible in 89765A4B if divisible by 9 and last digit even?
Answer: 3

Q21. (271 + 272 + 273 + 274) divisible by?
a) 9
b) 10
c) 11
d) 13
Answer: b) 10

Preparation Tips for Number System

  1. Revise divisibility rules (for 2, 3, 5, 7, 9, 11, 13, 24, etc.).

  2. Practice factorial zeros & factors daily.

  3. Do 10–15 PYQs under time constraints.

  4. Focus on logic-based questions — they repeat across exams.

Final Words

This Number System PYQ Super Set combines questions from multiple real exams. By practicing all these, you will gain the accuracy and speed required to clear the aptitude rounds of TCS, Infosys, Wipro, Accenture, Capgemini, and LTI Mindtree.