2017 AMC 8 Problem 21
Attempt Problem 21 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Suppose and are nonzero real numbers, and What are the possible value(s) for
and
and
, , and
, , and
Answer: A
Small hint:
Because , the three numbers cannot all have the same sign.
Big hint:
Each fraction is just the sign of .
Video solution:
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Written solution:
Because and none of the numbers is zero, their signs are either two positive and one negative or two negative and one positive. In the first case, the first three sign fractions sum to , while . In the second case, the first three sum to , while . Either way, the entire expression equals .
Thus, A is the correct answer.
Problem 21 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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- 1998 AMC 8
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