# 2021 JMPSC Sprint Problems/Problem 5

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## Problem

What two-digit even number has digits that sum to $17$?

## Solution

There exists a $2$ digit even number that has digits that sum to $17$. Pertaining to the assumption that this operation is in base $10$, there exists only $10$ digits to be used, specifically only $5$ for the first digit. Only $8$ and $9$ may be used, as there isn't other pair of digits which sum to $17$

The only two numbers in which satisfy the fact that the digits sum to $17$ are $98$ and $89$. Yet, only $98$ works because it is the only one in which satisfies the condition that the number must be even.

Therefore, $\boxed{98}$ is the only two-digit even number that has digits that sum to $17$.

-OofPirate

## Solution 2

The number must have digits $8$ and $9$. $89$ is odd but $\boxed{98}$ is even.

- kante314 -

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