2001 AMC 8 Problem 20
Attempt Problem 20 of the 2001 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 2001 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, “At least two of us have the same score.” Marty thinks, “I didn’t get the lowest score.” Shana thinks, “I didn’t get the highest score.” List the scores from lowest to highest for Marty (), Quay () and Shana ().
Answer: A
Small hint:
Quay only sees Kaleana’s score
Big hint:
Use each hidden-score statement relative to Kaleana
Solution:
Since Quay only knows Kaleana’s score, we get that Quay and Kaleana have the same score, so
Marty knows that his score is higher than Kaleana’s, so Shana knows that her score is lower than Kaleana’s, so
Substituting for we get the following inequality:
Thus, A is the correct answer.
Problem 20 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
- 1995 AMC 8
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- 1997 AMC 8
- 1998 AMC 8
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