Question

Question 30
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

The smallest pair of consecutive odd numbers is 1 and 3.
$\therefore$ Their sum=1+3=4, which is divisible by 4.

Let us take another example. Consider 41 and 43.
Their sum will be 41+ 43 = 84. This too is divisible by 4, giving a quotient of 21.

Now consider larger consecutive odd numbers like 1003 and 1005.
Their sum will be 1003 + 1005 = 2008. This is also divisible by 4 and gives a quotient of 502.

Therefore 4 is the largest number that always divides the sum of any two consecutive odd numbers.
Hence the correct answer is option B.