Difference between revisions of "2021 AMC 10B Problems/Problem 17"
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− | \text{Oscar's score is 4.} &\ | + | \text{Oscar's score is 4.} &\implies \text{Oscar is given cards 1 and 3.} \ |
− | &\ | + | &\implies \text{Aditi is given cards 2 and 5.} \ |
− | &\ | + | &\implies \text{Ravon is given cards 4 and 7.} \hspace{13mm} (*) \ |
− | &\ | + | &\implies \text{Tyrone is given cards 6 and 10.} \ |
− | &\ | + | &\implies \text{Kim is given cards 8 and 9.} |
\end{align*}</cmath> | \end{align*}</cmath> | ||
Revision as of 20:04, 12 April 2021
Contents
[hide]Problem
Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given cards out of a set of 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-- Oscar-- Aditi-- Tyrone-- Kim-- Which of the following statements is true?
Solution 1
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
Solution 3 (Comprehensive but Unnecessary)
By observations, we consider the scores from lowest to highest. We make the following logical deduction:
Therefore, the answer is
Of course, if we read the answer choices sooner, then we can stop at and pick
~MRENTHUSIASM
Video Solution by OmegaLearn (Using logical deduction)
~ pi_is_3.14
Video Solution by TheBeautyofMath
https://youtu.be/FV9AnyERgJQ?t=284
~IceMatrix
See Also
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 |
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