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Problem 645

AIME late

Algebra Difficulty 5.1 Find the answer

\section*{Problem 1 - V01001}

The digit sum of a two-digit number is 9. If you multiply the number by 5 and subtract 9 from the product, you get a two-digit number with the same digits in reverse order. What is the two-digit number?

Your answer

Official solution

}

We denote the two-digit number with $a$ . Due to the second condition, that $5 a-9<100$ must hold, $a<22$ must be true. Therefore, the candidate we are looking for is 18, since

$5 \cdot 18-9=90-9=81$

satisfies the second condition and 18 has a digit sum of 9.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.