# Find all pairs of consecutive odd natural number,

Question:

Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.

Solution:

Let x be the smaller of the two odd natural numbers. Then, the other odd natural number will be x + 2.
Therefore, as per the given conditions:

$x>10$ and $x+x+2<40$

$\Rightarrow x>10$ and $2 x+2<40$

$\Rightarrow x>10$ and $x<19$

$\Rightarrow 10$\therefore x \in\{11,13,15,17\}$Hence, the pairs are$(11,13),(13,15),(15,17),(17,19)\$.