Question

The largest number which always divides the sum of any pair of consecutive odd numbers is (A) 2 (B) 4 (C) 6 (D) 8

Answer 1

(B) 4.

Explanation:

The largest number that always divides the sum of any pair of consecutive odd numbers can be determined by observing a pattern.

Let's consider a pair of consecutive odd numbers, such as 3 and 5. The sum of these numbers is 3 + 5 = 8.

Now, let's consider another pair of consecutive odd numbers, such as 7 and 9. The sum of these numbers is 7 + 9 = 16.

If we continue this pattern, we can see that the sum of any pair of consecutive odd numbers will always be divisible by 4.

For example:

- 9 + 11 = 20 (divisible by 4)

- 15 + 17 = 32 (divisible by 4)

- 21 + 23 = 44 (divisible by 4)

Therefore, the largest number that always divides the sum of any pair of consecutive odd numbers is 4.