Question

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

Answer 1

Let x and x+2 be two consecutive even positive integers Then x > 5 and x+x+2 <23

$\Rightarrow x>5$ and 2x+2 <23

$\Rightarrow x>5$ and 2x < 23 -2

$\Rightarrow x>5$ and 2x < 21

$\Rightarrow x>5$ and $x<\frac{21}{2}$

$\Rightarrow 5<x<\frac{21}{2}\Rightarrow x=6,8,10$

Thus required pairs of even positive integers are (6,8)(8,10) and (10,12).