Distinct values of N

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 $N$?

Accepted Answer

6. Since $x$ and $y$ are positive integers: $3 \le x \le 9$ $15 \le y \le 22$ Minimum value of $N = 3 + 15 = 18$. Maximum value of $N = 9 + 22 = 31$. We are given $N > 25$, so possible integer values of $N$ range from $26$ to $31$. All values between $26$ and $31$ (inclusive) can be achieved by picking suitable $x$ and $y$. Number of distinct values = $31 - 26 + 1 = 6$.

Answer

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Distinct values of N

Explanation

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