Question

The product of two consecutive positive integers is divisible by $2$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the 2 consecutive numbers be, $x,x+1$

product of these consecutive numbers, $=x(x+1)$

(1) even

let, $x=2k$

product $=2k[2k+1]$

from above equation it is clear that the product is divisible by 2

(2) odd

let, $x=2k+1$

product $=(2k+1)\left[\right(2k+1)+1]$

$=2(2k^2+3k+1)$

from above equation it is clear that the product is divisible by 2