# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 5"

## 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 -
The text passage contains a mathematical question and provides an answer to it. The question asks for a two-digit even number whose digits sum to 17, and the answer given is 98.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Difference between revisions of "2021 JMPSC Sprint Problems/Problem 5"

## 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 -
user
The text passage contains a mathematical question and provides an answer to it. The question asks for a two-digit even number whose digits sum to 17, and the answer given is 98.

TYPE: SINGLE_QUESTION_WITH_ANSWER