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CAT 2020 Slot 3 QA Question & Solution

Number SystemsHard

Question

Let $N$, $x$ and $y$ be positive integers such that $N=x+y$, ${ }$ $2\lt x \lt 10$ ${ }$ and ${ }$ $14 \lt y \lt 23$. If $N \gt25$, then how many distinct values are possible for N?

Solution

Possible values of x = 3,4,5,6,7,8,9

When x = 3, there is no possible value of y

When x = 4, the possible values of y = 22

When x = 5, the possible values of y=21, 22

When x = 6, the possible values of y = 20, 21, 22

When x = 7, the possible values of y = 19, 20, 21, 22

When x = 8, the possible values of y=18, 19, 20, 21, 22

When x = 9, the possible values of y=17, 18, 19, 20, 21, 22

The unique values of N = 26, 27, 28, 29, 30, 31