1986 AMC 8 Problem 17
Attempt Problem 17 of the 1986 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 1986 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
Let be an odd whole number and let be any whole number. Which of the following statements about the whole number is always true?
it is always odd
it is always even
it is even only if is even
it is odd only if is odd
it is odd only if is even
Small hint:
Factor:
Big hint:
Since is odd, the parity of matches the parity of
Solution:
Factor Because is odd, the product is odd exactly when is odd, which happens only when is even. When is odd, is even and the product is even.
So the number is odd only if is even.
Thus, the correct answer is E .
Problem 17 in other years
- 1985 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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