2014 AMC 8 Problem 22

Attempt Problem 22 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.

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22.

A $2$ -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?

$1$

$3$

$5$

$7$

$9$

Let the number be $10a+b$ , where $a$ is the tens digit and $b$ is the units digit. The condition gives $ab+a+b=10a+b.$

Canceling $b$ from both sides gives $ab+a=10a$ , so $ab=9a$ . Since $a\neq0$ , we get $b=9$ .

Thus, E is the correct answer.