1985 AMC 8 Problem 25
Attempt Problem 25 of the 1985 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 1985 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Five cards are lying on a table. Each card has a letter on one side and a whole number on the other side. The visible faces show and Jane said, “If a vowel is on one side of any card, then an even number is on the other side.” Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?
Answer: A
Small hint:
To disprove the rule, find a card that could hide a vowel paired with an odd number
Big hint:
No vowel is visible ( and are consonants), so the card to check is the one showing an odd number
Solution:
To show the rule “a vowel forces an even number” is false, Mary needs a card with a vowel on one side and an odd number on the other. No card shows a vowel, since and are consonants.
The only card showing an odd number is Turning it over reveals a vowel, which contradicts Jane’s claim.
Thus, the correct answer is A .
Problem 25 in other years
- 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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