2013 AMC 8 Problem 13
Attempt Problem 13 of the 2013 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
13.
When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of one score. By which of the following might her incorrect sum have differed from the correct one?
Answer: A
Small hint:
Reversing tens and units changes a number by a multiple of .
Big hint:
Check which answer choice is divisible by .
Video solution:
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Written solution:
If the last two digits of the score are , then reversing those digits gives . The difference is so the incorrect sum must differ from the correct sum by a multiple of .
Among the answer choices, only is divisible by .
Thus, A is the correct answer.
Problem 13 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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