CAT 2020 Slot 3 QA Question 14: Let $N$, $x$ and $y$ be positive integers such that $N = x + y$, $2 25$, then how many distinct values are possible for $N$?

Question

Let $N$, $x$ and $y$ be positive integers such that $N = x + y$, $2  25$, then how many distinct values are possible for $N$?

Accepted Answer

The possible values are $x = 3, 4, 5, 6, 7, 8, 9$ and $y = 15, 16, \ldots, 22$.
The maximum possible value of $N$ is $9 + 22 = 31$.
Since $N > 25$, the least possible value of $N$ is 26. Every integer from 26 to 31 is achievable by suitable choices of $x$ and $y$.
Possible values of $N = 26, 27, 28,

Let NNN, xxx and yyy be positive integers such that N=x+yN = x + yN=x+y, 2<x<102 < x < 102<x<10 and 14<y<2314 < y < 2314<y<23. If N>25N > 25N>25, then how many distinct values are possible for NNN?

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 $N$ ?