Question

The difference of the squares of two consecutive even integers is divisible by which of the following integers. (a). 3. ( b). 4 ( c). 6. (d). 7. Plz give the answer with the solution.

Answer 1

Lets take examples
4²-2²=16-4=12
6²-4²=36-16=20
8²-6²=64-36=28
10²-8²=100-64=36

The common divident of all the nos. 12, 20, 28, 36 is 4
Ans.(b)4

If found useful please choose it the best answer.
By
MASelvam
Booksworm

Answer 2

The difference of the squares of two consecutive even integers is divisible by 4 i.e, option (b)

Let the two consecutive even integers be 2x, 2x+2

Their squares are $(2x)^{2}$ and $(2x+2)^{2}$

Difference of their squares is given by

              $(2x+2)^{2}$ - $(2x)^{2}$

           = $4x^{2} + 4 + 8x - 4x^{2}$

           = 8x + 4

           = 4(2x + 1)

Therefore, the correct option is (b)