Question

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Answer 1

Let x and x+2 be two consecutive odd positive integers

Then x+2 < 10 and x+x+2 >11.

$\Rightarrow x<8$ and 2x+2 > 11

$\Rightarrow x<8$ and 2x > -2 +11

$\Rightarrow x<8$ and 2x > 9

$\Rightarrow x<8$ and $x>\frac{9}{2}$

$\Rightarrow \frac{9}{2}<x<8\Rightarrow x=5$ and 7

Thus required pairs of odd positive integers are (5,7) and (7,9).