2010 AMC 8 Problem 22
Attempt Problem 22 of the 2010 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 2010 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
The hundreds digit of a three-digit number is more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
Answer: E
Small hint:
The tens digit cancels when the reversed number is subtracted.
Big hint:
Represent the original number with hundreds digit two more than the units digit.
Solution:
Let the units digit be and let the tens digit be This makes the hundreds digit be This makes the number equal to and the reversed number is This makes the difference equal to This makes the units digit
Therefore, the answer is E .
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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