NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice QuestionsQuestion 30
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question. 30
The largest number that always divides the sum of any pair of consecutive odd numbers is
(A)
2
(B)
4
(C)
6
(D)
8
Detailed Answer with Explanation:
Step 1: Write two consecutive odd numbers in general form.
First odd number: \(2n + 1\)
Next odd number: \(2n + 3\)
Step 2: Add them.
\((2n + 1) + (2n + 3)\)
= \(2n + 2n + 1 + 3\)
= \(4n + 4\)
Step 3: Factor the sum.
\(4n + 4 = 4(n + 1)\)
What this means: The sum is always a multiple of 4, because it is \(4 \times (n+1)\).
Step 4 (check bigger options): Is it always divisible by 8?
Try examples:
\(3 + 5 = 8\) (divisible by 8)
\(5 + 7 = 12\) (not divisible by 8)
So 8 does not always divide the sum.
Conclusion: The largest number that always divides the sum is \(\boxed{4}\).