NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question 16

Question.  16

The product of a non-zero whole number and its successor is always

(A)

an even number

(B)

an odd number

(C)

a prime number

(D)

divisible by 3

Detailed Answer with Explanation:

Idea: Two numbers that come one after the other are called consecutive. Examples: (1, 2), (5, 6), (10, 11).

Let the whole number be \(n\). Because it is non-zero, \(n \ge 1\).

Its successor (the next number) is \(n + 1\).

Among any two consecutive numbers, one is always even.

Case 1: If \(n\) is even, then \(n = 2k\) for some whole number \(k\).

Case 2: If \(n\) is odd, then \(n = 2k + 1\). The next number is \(n+1 = 2k + 2 = 2(k+1)\), which is even.

So in both cases, at least one of \(n\) or \(n+1\) is a multiple of \(2\).

Therefore, their product has a factor \(2\): \(n(n+1)\) is even.

Quick check with examples:

\(3 \times 4 = 12\) (even),   \(6 \times 7 = 42\) (even)

Conclusion: The product is always an even number (Option A).

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – Multiple Choice Questions | Detailed Answers