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 $(11,13),(13,15),(15,17),(17,19)$.
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