Test: Number Play - Class 8 MCQ

Powers of 2 (like 2, 4, 8, 16, 32…) cannot be expressed as a sum of consecutive natural numbers.

There are 2 possible signs (+ or –) at 2 places, so total expressions = 2² = 4. But with 3 numbers, there are 2 gaps, so 2² = 4. Oops wait correction: Actually between 3 numbers, there are 2 sign positions → 2² = 4.
Correct Option: a) 4

Multiplying any number with an even number always gives an even product.

The form 2n + 1 always gives an odd number for any integer n.

6 = 2 × 3, 8 = 2³ → LCM = 2³ × 3 = 24.

Example: 2, 9, 16, 23… all are of the form 7k + 2.

A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.

Rule: Divisible by 6 ⇔ divisible by 2 and 3.

4+7+2+5=18 → 1+8=9.

(1+0) – (0+1) = 0, divisible by 11 → so 1001 is divisible by 11.

n² + n = n(n+1), product of two consecutive numbers → always even.

Any power of 10 gives remainder 1 when divided by 9.

Only option c satisfies (two-digit × 9 = three-digit, distinct digits).

GCD(8,25) = 1 → co-prime.

Divisibility rule: If sum of digits is divisible by 9, then number is divisible by 9.