Basic Numeracy (Class X Level) – Number system and number relations

Assam Public Service Commission (APSC)

Combined Competitive Examination (CCE)

Preliminary Examination – General Studies Paper II (Objective Type, 200 Marks)

Topic: Basic Numeracy (Class X Level)

Sub-Topic: Number System and Number Relations

These questions test concepts of natural numbers, whole numbers, integers, rational & irrational numbers, divisibility, prime–composite relations, HCF & LCM, and numerical relationships. Choose the correct answer.

Number System & Number Relations – MCQs

MCQ 1

Which of the following is a natural number?
A. −1
B. 0
C. 1
D. −5

Correct Answer: C
Explanation: Natural numbers start from 1, 2, 3, ….

MCQ 2

Which of the following is not a whole number?
A. 0
B. 5
C. 12
D. −3

Correct Answer: D
Explanation: Whole numbers include 0 and positive integers, not negatives.

MCQ 3

Which number is an integer?
A. 2.5
B. −7
C. 3⁄4
D. √2

Correct Answer: B
Explanation: Integers include negative, zero, and positive whole numbers.

MCQ 4

Which of the following is a rational number?
A. √3
B. π
C. 0.25
D. √5

Correct Answer: C
Explanation: 0.25 = 1⁄4, which is a ratio of integers.

MCQ 5

Which of the following is an irrational number?
A. 4
B. 0.5
C. √2
D. −3

Correct Answer: C
Explanation: √2 cannot be expressed as p⁄q.

MCQ 6

The smallest prime number is:
A. 0
B. 1
C. 2
D. 3

Correct Answer: C
Explanation: 2 is the smallest and the only even prime number.

MCQ 7

Which of the following is a composite number?
A. 2
B. 3
C. 5
D. 9

Correct Answer: D
Explanation: 9 has more than two factors (1, 3, 9).

MCQ 8

Which number has exactly two factors?
A. 1
B. Prime number
C. Composite number
D. Even number

Correct Answer: B
Explanation: Prime numbers have exactly two distinct factors.

MCQ 9

The HCF of 12 and 18 is:
A. 2
B. 3
C. 6
D. 12

Correct Answer: C
Explanation: Common factors: 1, 2, 3, 6 → Highest is 6.

MCQ 10

The LCM of 6 and 8 is:
A. 12
B. 24
C. 48
D. 16

Correct Answer: B
Explanation: LCM = 2³ × 3 = 24.

MCQ 11

If HCF × LCM = product of two numbers, then for numbers 8 and 12:
LCM = ?
A. 12
B. 24
C. 36
D. 48

Correct Answer: B
Explanation: HCF = 4 → 4 × LCM = 96 → LCM = 24.

MCQ 12

Which of the following is divisible by 3?
A. 1,234
B. 2,345
C. 4,567
D. 3,333

Correct Answer: D
Explanation: Sum of digits = 12, divisible by 3.

MCQ 13

Which number is divisible by 11?
A. 1,331
B. 2,222
C. 3,344
D. 4,455

Correct Answer: A
Explanation: Difference of alternating digits = 0.

MCQ 14

Which of the following is an even number?
A. 15
B. 27
C. 42
D. 35

Correct Answer: C
Explanation: Even numbers are divisible by 2.

MCQ 15

The number 0 is:
A. Prime
B. Composite
C. Neither prime nor composite
D. Natural number

Correct Answer: C
Explanation: 0 has infinite divisors; it is neither.

MCQ 16

Which of the following pairs are co-prime?
A. 6 and 9
B. 8 and 12
C. 9 and 28
D. 15 and 25

Correct Answer: C
Explanation: HCF of 9 and 28 = 1.

MCQ 17

If a number is divisible by 2 and 3, it is divisible by:
A. 4
B. 5
C. 6
D. 9

Correct Answer: C
Explanation: Divisibility by 2 and 3 implies divisibility by 6.

MCQ 18

Which of the following is a perfect square?
A. 16
B. 20
C. 24
D. 28

Correct Answer: A
Explanation: 16 = 4².

MCQ 19

The additive identity in the number system is:
A. 1
B. −1
C. 0
D. 10

Correct Answer: C
Explanation: Adding 0 leaves a number unchanged.

MCQ 20

The multiplicative identity is:
A. 0
B. 1
C. −1
D. 10

Correct Answer: B
Explanation: Any number × 1 = same number.

MCQ 21

Which number lies between −2 and 1?
A. −3
B. −1
C. 2
D. 3

Correct Answer: B
Explanation: −1 lies between −2 and 1.

MCQ 22

Which of the following is the smallest integer?
A. −100
B. 0
C. 1
D. No smallest integer

Correct Answer: D
Explanation: Integers extend infinitely in the negative direction.

MCQ 23

If a = 5 and b = −3, then a − b equals:
A. 2
B. −2
C. 8
D. −8

Correct Answer: C
Explanation: 5 − (−3) = 5 + 3 = 8.

MCQ 24

Which number has the maximum value?
A. −7
B. −2
C. 0
D. −10

Correct Answer: C
Explanation: 0 is greater than all negative numbers.

MCQ 25

If a number leaves remainder 1 when divided by 2, it is:
A. Even
B. Prime
C. Odd
D. Composite

Correct Answer: C
Explanation: Odd numbers leave remainder 1 on division by 2.

MCQ 26

Which of the following is a terminating decimal?
A. 1⁄3
B. 2⁄7
C. 5⁄8
D. 7⁄9

Correct Answer: C
Explanation: 5⁄8 = 0.625 (terminating).

MCQ 27

The reciprocal of −4 is:
A. 4
B. −4
C. −1⁄4
D. 1⁄4

Correct Answer: C
Explanation: Reciprocal of a number x is 1⁄x.

MCQ 28

Which of the following numbers has exactly three factors?
A. 4
B. 6
C. 8
D. 9

Correct Answer: A
Explanation: 4 has factors 1, 2, 4.

MCQ 29

If the product of two numbers is 0, then:
A. Both numbers are zero
B. At least one number is zero
C. Both numbers are non-zero
D. Both are negative

Correct Answer: B
Explanation: Zero-product rule.

MCQ 30

Number relations in basic numeracy mainly test:
A. Memorization
B. Approximation
C. Logical understanding of numbers
D. Language skills

Correct Answer: C
Explanation: This topic focuses on properties and relationships among numbers.

✅ APSC Exam Relevance

These MCQs comprehensively cover number classification, divisibility, HCF–LCM, rational–irrational distinction, and numerical relationships, strictly aligned with APSC CCE GS Paper II – Basic Numeracy (Class X level).

• Number system questions for competitive exams

• Basic numeracy MCQs GS Paper II

• Number relations and divisibility MCQs

• HCF and LCM questions APSC CCE

• Rational and irrational numbers MCQs