Difference between revisions of "2021 AMC 10B Problems/Problem 17"
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~smarty101 and smartypantsno_3 | ~smarty101 and smartypantsno_3 | ||
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| + | ==Solution 2== | ||
| + | Oscar must be given 3 and 1. Aditi cannot be given 3 or 1, so she must have 2 and 5. Similarly, Ravon cannot be given 1, 2, 3, or 5, so he must have 4 and 7, and the answer is <math>\boxed{ \textbf{(C) \ }\text{Ravon was given card 4.}}</math>. | ||
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| + | -SmileKat32 | ||
{{AMC10 box|year=2021|ab=B|num-b=16|num-a=18}} | {{AMC10 box|year=2021|ab=B|num-b=16|num-a=18}} | ||
Revision as of 07:34, 12 February 2021
Problem
Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given 2 cards out of a set of 10 cards numbered 
The score of a player is the sum of the numbers of their cards. The scores of the players are as follows: Ravon--11, Oscar--4, Aditi--7, Tyrone--16, Kim--17. Which of the following statements is true?
Solution
Oscar must be given 3 and 1, so we rule out 
and 
. If Tyrone had card 7, then he would also have card 9, and then Kim must have 10 and 7 so we rule out 
. If Aditi was given card 4, then she would have card 3, which Oscar already had. So the answer is 
~smarty101 and smartypantsno_3
Solution 2
Oscar must be given 3 and 1. Aditi cannot be given 3 or 1, so she must have 2 and 5. Similarly, Ravon cannot be given 1, 2, 3, or 5, so he must have 4 and 7, and the answer is .
-SmileKat32
| 2021 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 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 AMC 10 Problems and Solutions | ||
