Practice number system MCQ with answers and clear explanations to prepare for SSC, banking, and other competitive exams easily.
If you are preparing for competitive exams, you already know how important the number system topic is. Questions from this chapter appear frequently in aptitude tests, school exams, and entrance papers. Most of these questions are asked in number system mcq format, where clarity matters more than lengthy calculations.
In this section, you get carefully selected number system questions designed to test your understanding of concepts like integers, rational numbers, divisibility, and place value. Each question comes with clear options and a direct answer so you can check your logic instantly. These number system questions and answers also work well as number system practice questions for revision.
Number System MCQs
- If a number is increased by 20%, by what percent should it be decreased to get the original number?
A) 16⅔%
B) 18%
C) 20%
D) 25%
Answer: A
- The sum of two numbers is 27 and their product is 182. What is the difference between the numbers?
A) 1
B) 5
C) 9
D) 13
Answer: B
- If x² − 15x + 56 = 0, then the value of x³ − 56/x is
A) 343
B) 512
C) 169
D) 729
Answer: A
- How many two-digit numbers are divisible by 7 but not divisible by 5?
A) 11
B) 12
C) 13
D) 14
Answer: B
- The product of three consecutive positive integers is 1320. What is the middle number?
A) 10
B) 11
C) 12
D) 13
Answer: C
- What least number must be added to 3275 to make it divisible by 18?
A) 5
B) 7
C) 9
D) 11
Answer: B
- If the HCF of two numbers is 12 and their LCM is 1800, how many such pairs are possible?
A) 2
B) 3
C) 4
D) 5
Answer: C
- The number of trailing zeros in 125! is
A) 28
B) 29
C) 30
D) 31
Answer: C
- If 7ⁿ⁺¹ + 7ⁿ = 392, find the value of n
A) 1
B) 2
C) 3
D) 4
Answer: B
- The remainder when 7²⁰⁰ is divided by 6 is
A) 1
B) 3
C) 5
D) 0
Answer: A
- What is the smallest number which when divided by 12, 15, and 20 leaves remainder 5 each time?
A) 125
B) 185
C) 245
D) 305
Answer: C
- If √(x − 3) + √(x − 8) = 7, then x equals
A) 12
B) 15
C) 18
D) 20
Answer: C
- How many digits are there in 2⁶⁴?
A) 18
B) 19
C) 20
D) 21
Answer: C
- A number when divided by 4 gives remainder 3. What will be the remainder when its square is divided by 8?
A) 1
B) 3
C) 5
D) 7
Answer: D
- What is the greatest 5-digit number divisible by 16?
A) 99984
B) 99968
C) 99952
D) 99936
Answer: B
- If (2ˣ + 2ˣ⁺¹) = 96, then x equals
A) 4
B) 5
C) 6
D) 7
Answer: B
- The sum of the first n natural numbers is 210. What is the value of n?
A) 19
B) 20
C) 21
D) 22
Answer: C
- The smallest number which is divisible by all numbers from 1 to 10 is
A) 2520
B) 1260
C) 5040
D) 10080
Answer: A
- If a number is divisible by 12 and 18, then it must be divisible by
A) 6
B) 24
C) 36
D) 72
Answer: C
- What is the remainder when (17³ + 19³) is divided by 9?
A) 0
B) 1
C) 2
D) 4
Answer: A
- How many factors does 360 have?
A) 20
B) 22
C) 24
D) 28
Answer: C
- If a number is multiplied by 5/8, it becomes 60. What is the number?
A) 72
B) 84
C) 96
D) 108
Answer: C
- The difference between the squares of two consecutive natural numbers is 71. What is the smaller number?
A) 34
B) 35
C) 36
D) 37
Answer: B
- What least number should be multiplied to 90 to make it a perfect cube?
A) 2
B) 3
C) 5
D) 6
Answer: C
- If the ratio of two numbers is 3:5 and their LCM is 180, what is their HCF?
A) 6
B) 9
C) 12
D) 15
Answer: B
- The value of (999)² − (998)² is
A) 1997
B) 1998
C) 1999
D) 2000
Answer: C
- How many numbers between 1 and 1000 are divisible by 7 but not by 14?
A) 71
B) 72
C) 73
D) 74
Answer: A
- The sum of all prime numbers between 10 and 30 is
A) 112
B) 119
C) 129
D) 139
Answer: B
- What is the unit digit of 3¹⁰³?
A) 1
B) 3
C) 7
D) 9
Answer: D
- If a number is divided by 45, the remainder is 17. What will be the remainder when the same number is divided by 15?
A) 1
B) 2
C) 3
D) 7
Answer: B
- If the product of two numbers is 2028 and their HCF is 13, what is their LCM?
A) 52
B) 78
C) 156
D) 2028
Answer: C
- The sum of digits of a two-digit number is 9. If the digits are reversed, the number becomes 27 more than the original. The number is
A) 36
B) 45
C) 54
D) 63
Answer: B
- How many numbers between 1 and 500 are divisible by 5 but not divisible by 10?
A) 25
B) 50
C) 75
D) 100
Answer: B
- If (2ⁿ + 2ⁿ⁺²) = 80, then the value of n is
A) 3
B) 4
C) 5
D) 6
Answer: B
- The number of zeros at the end of 100! is
A) 22
B) 23
C) 24
D) 25
Answer: D
- What is the remainder when 13⁹⁹ is divided by 12?
A) 0
B) 1
C) 11
D) 13
Answer: B
- The smallest number which leaves remainder 3 when divided by 7, 9, and 11 is
A) 696
B) 693
C) 675
D) 693 + 3
Answer: D
- If x = 2 + √3, then the value of x² + 1/x² is
A) 14
B) 10
C) 7
D) 8
Answer: B
- How many digits are there in 5¹²⁵?
A) 86
B) 87
C) 88
D) 89
Answer: C
- The greatest number that divides 1224, 1572, and 1908 exactly is
A) 36
B) 48
C) 60
D) 72
Answer: B
- The remainder when (6¹⁰ + 8¹⁰) is divided by 7 is
A) 0
B) 1
C) 2
D) 6
Answer: A
- What least number must be multiplied to 360 to make it a perfect square?
A) 2
B) 3
C) 5
D) 10
Answer: C
- If the ratio of two numbers is 4:7 and their difference is 81, what is the larger number?
A) 189
B) 196
C) 203
D) 210
Answer: C
- The sum of first 50 odd numbers is
A) 2500
B) 2550
C) 2600
D) 2700
Answer: A
- If a number is divisible by 18 and 24, then it must be divisible by
A) 6
B) 12
C) 36
D) 72
Answer: C
- The unit digit of (7²⁵ × 3³⁴) is
A) 1
B) 3
C) 7
D) 9
Answer: D
- The sum of three consecutive even numbers is 84. The smallest number is
A) 26
B) 28
C) 30
D) 32
Answer: B
- What is the least number which when divided by 8, 12, and 20 leaves remainder 7?
A) 247
B) 247 + 1
C) 240
D) 247 − 1
Answer: A
- If x² − 9x + 20 = 0, then the value of (x₁² + x₂²) is
A) 41
B) 49
C) 61
D) 81
Answer: A
- How many factors does 840 have?
A) 24
B) 28
C) 32
D) 36
Answer: B
- The remainder when 4⁵⁰ is divided by 15 is
A) 1
B) 4
C) 6
D) 10
Answer: A
- The smallest number which is a perfect square and divisible by 72 is
A) 144
B) 288
C) 432
D) 576
Answer: D
- If the sum of reciprocals of two numbers is 1/6 and their difference is 6, the larger number is
A) 18
B) 12
C) 9
D) 8
Answer: A
- The value of (9999² − 9998²) is
A) 19997
B) 19998
C) 19999
D) 20000
Answer: C
- The number of integers between −100 and 100 divisible by 7 is
A) 28
B) 29
C) 30
D) 31
Answer: B
- The sum of all prime numbers less than 50 is
A) 306
B) 328
C) 381
D) 396
Answer: B
- The value of log₁₀(1000) is
A) 2
B) 3
C) 4
D) 10
Answer: B
- The smallest 6-digit number divisible by 91 is
A) 100009
B) 100191
C) 100282
D) 100373
Answer: A
- If n is a natural number such that n² + n is even, then n must be
A) Even
B) Odd
C) Prime
D) Composite
Answer: A
- The remainder when (2⁵⁰ + 3⁵⁰) is divided by 5 is
A) 0
B) 1
C) 2
D) 4
Answer: A
Conclusion
The number system is one of the most important topics in competitive examinations, and mastering it requires more than memorising formulas. Through these number system MCQs, you practiced a wide range of concepts, including divisibility, remainders, powers, HCF and LCM, factorials, and digit-based logic. These questions are designed to sharpen your thinking and help you identify patterns quickly.
By regularly solving such number system questions and answers, you improve accuracy and reduce the chances of making careless mistakes. Consistent practice with number system practice questions also builds confidence, especially when facing time-bound exams. Keep revising these MCQs, focus on understanding the logic behind each answer, and you will be well prepared to handle even the toughest number system questions in your exam.
