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

Le x be the smaller of the two consecutive even positive integers.

Then the other even integer is x+2.

It is given that both the even integers are greater than 5 and their sum is less than 23.

$\therefore x>5and,x+x+2<23\Rightarrow x>5and2x<21\Rightarrow x>5andx<\frac{21}{2}\Rightarrow 5<x<\frac{21}{2}=10.5\Rightarrow x=6,8,10[\because xisaneveninteger]\text{Hence,the required pairs of odd natural integers are (6,8),(8,10)~and~(10,12).}$