Question

Let $N$, $x$ and $y$ be positive integers such that $N=x+y$, $2<x<10$ and $14<y<23$. If $N>25$, then how many distinct values are possible for $N$?

Answer 1

Given, $2<x<10$ and $14<y<23$ $⇒17 <(x+y)<32$ i.e. $17<N<32$

But $N>25$

Hence $25<N<32$

$N$ can take $6$ distinct values.