Difference between revisions of "2021 AMC 10B Problems/Problem 17"
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Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given 2 cards out of a set of 10 cards numbered <math>1,2,3, \dots,10.</math> 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? | Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given 2 cards out of a set of 10 cards numbered <math>1,2,3, \dots,10.</math> 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? | ||
| − | <math> \textbf{(A) \ }\text{Ravon was given card 3.} \qquad \textbf{(B) \ }\text{Aditi was given card 3.} \qquad \textbf{(C) \ }\text{Ravon was given card 4.} \qquad \textbf{(D) \ }\text{Aditi was given card 4} \qquad </math> <math> \textbf{(E) \ }\text{Tyrone was | + | <math> \textbf{(A) \ }\text{Ravon was given card 3.} \qquad \textbf{(B) \ }\text{Aditi was given card 3.} \qquad \textbf{(C) \ }\text{Ravon was given card 4.} \qquad \textbf{(D) \ }\text{Aditi was given card 4} \qquad </math> <math> \textbf{(E) \ }\text{Tyrone was given card 7} </math> |
==Solution== | ==Solution== | ||
Revision as of 12:31, 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 | |
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| All AMC 10 Problems and Solutions | ||
