Difference between revisions of "1985 AJHSME Problems/Problem 25"
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\boxed{\tt{3}} & \qquad & \boxed{\tt{4}} & \qquad & \boxed{\tt{6}} \end{matrix}</cmath> | \boxed{\tt{3}} & \qquad & \boxed{\tt{4}} & \qquad & \boxed{\tt{6}} \end{matrix}</cmath> | ||
| − | Each card has a letter on one side and a whole number on the other side. 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? | + | Each card has a letter on one side and a [[whole number]] on the other side. 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? |
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ \text{P} \qquad \text{(E)}\ \text{Q}</math> | <math>\text{(A)}\ 3 \qquad \text{(B)}\ 4 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ \text{P} \qquad \text{(E)}\ \text{Q}</math> | ||
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If an even number is not on one side of any card, then a vowel is not on the other side. | If an even number is not on one side of any card, then a vowel is not on the other side. | ||
| − | For Mary to show Jane wrong, she must find a card with an odd number on one side, and a vowel on the other side. The only card that could possibly have this property is the card with <math>3</math>, which is answer choice <math>\boxed{\text{A}}</math> | + | For Mary to show Jane wrong, she must find a card with an [[odd number]] on one side, and a vowel on the other side. The only card that could possibly have this property is the card with <math>3</math>, which is answer choice <math>\boxed{\text{A}}</math> |
==See Also== | ==See Also== | ||
| − | + | {{AJHSME box|year=1985|num-b=24|after=Last<br>Problem}} | |
| − | |||
[[Category:Logic Problems]] | [[Category:Logic Problems]] | ||
Revision as of 17:48, 18 May 2009
Problem
Five cards are lying on a table as shown.
![\[\begin{matrix} & \qquad & \boxed{\tt{P}} & \qquad & \boxed{\tt{Q}} \\ \\ \boxed{\tt{3}} & \qquad & \boxed{\tt{4}} & \qquad & \boxed{\tt{6}} \end{matrix}\]](http://latex.artofproblemsolving.com/f/a/e/fae700ade12943277f8147039b058865f3fff819.png)
Each card has a letter on one side and a whole number on the other side. 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?
Solution
Logically, Jane's statement is equivalent to its contrapositive,
If an even number is not on one side of any card, then a vowel is not on the other side.
For Mary to show Jane wrong, she must find a card with an odd number on one side, and a vowel on the other side. The only card that could possibly have this property is the card with 
, which is answer choice 
See Also
| 1985 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
