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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
A -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?
Answer: E
Small hint:
Let the tens digit be and the units digit be .
Big hint:
Translate the condition into .
Solution:
Let the number be , where is the tens digit and is the units digit. The condition gives
Canceling from both sides gives , so . Since , we get .
Thus, E is the correct answer.
Problem 22 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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- 1993 AMC 8
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