1987 AMC 8 Problem 20
Attempt Problem 20 of the 1987 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 1987 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
Consider the statement: “If a whole number is not prime, then the whole number is not prime.” Which of the following values of shows this statement to be false?
Answer: A
Small hint:
To disprove an “if ... then” statement, find a case where the “if” part holds but the “then” part fails
Big hint:
Look for that is not prime while is prime
Solution:
A counterexample needs not prime but prime. For the number is not prime while is prime, so it breaks the statement.
The others fail to be counterexamples: and are not prime, while and are themselves prime.
Thus, the correct answer is A .
Problem 20 in other years
- 1985 AMC 8
- 1986 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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