2021 AMC 10B Problems/Problem 17
Contents
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
Video Solution by OmegaLearn (Using logical deduction)
~ pi_is_3.14
Video Solution by TheBeautyofMath
https://youtu.be/FV9AnyERgJQ?t=284
~IceMatrix
2021 AMC 10B (Problems • Answer Key • Resources) | ||
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Followed by Problem 18 | |
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