Difference between revisions of "2021 AMC 10B Problems/Problem 17"
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| − | + | ==Problem== | |
| − | + | ||
| + | Ravon, Oscar, Aditi, Tyrone, and Kim play a card game. Each person is given <math>2</math> cards out of a set of <math>10</math> 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--<math>11,</math> Oscar--<math>4,</math> Aditi--<math>7,</math> Tyrone--<math>16,</math> Kim--<math>17.</math> Which of the following statements is true? | ||
| + | |||
| + | <math>\textbf{(A) }\text{Ravon was given card 3.}</math> | ||
| + | |||
| + | <math>\textbf{(B) }\text{Aditi was given card 3.}</math> | ||
| + | |||
| + | <math>\textbf{(C) }\text{Ravon was given card 4.}</math> | ||
| + | |||
| + | <math>\textbf{(D) }\text{Aditi was given card 4.}</math> | ||
| + | |||
| + | <math>\textbf{(E) }\text{Tyrone was given card 7.}</math> | ||
| + | |||
| + | ==Solution== | ||
| + | By logical deduction, we consider the scores from lowest to highest: | ||
| + | <cmath>\begin{align*} | ||
| + | \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.} && (\bigstar) \\ | ||
| + | &\implies \text{Tyrone is given cards 6 and 10.} \\ | ||
| + | &\implies \text{Kim is given cards 8 and 9.} | ||
| + | \end{align*}</cmath> | ||
| + | Therefore, the answer is <math>\boxed{\textbf{(C) }\text{Ravon was given card 4.}}</math> | ||
| + | |||
| + | Certainly, if we read the answer choices sooner, then we can stop at <math>(\bigstar)</math> and pick <math>\textbf{(C)}.</math> | ||
| + | |||
| + | ~smarty101 ~smartypantsno_3 ~SmileKat32 ~MRENTHUSIASM | ||
| + | |||
| + | == Video Solution by OmegaLearn (Using Logical Deduction) == | ||
| + | https://youtu.be/zO0EuKPXuT0 | ||
| + | |||
| + | ~ pi_is_3.14 | ||
| + | |||
| + | ==Video Solution by TheBeautyofMath== | ||
| + | https://youtu.be/FV9AnyERgJQ?t=284 | ||
| + | |||
| + | ~IceMatrix | ||
| + | ==Video Solution by Interstigation== | ||
| + | https://youtu.be/8BPKs24eyes | ||
| + | |||
| + | ~Interstigation | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2021|ab=B|num-b=16|num-a=18}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 15:18, 6 November 2021
Contents
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
By logical deduction, we consider the scores from lowest to highest:
Therefore, the answer is 
Certainly, if we read the answer choices sooner, then we can stop at 
and pick 
~smarty101 ~smartypantsno_3 ~SmileKat32 ~MRENTHUSIASM
Video Solution by OmegaLearn (Using Logical Deduction)
~ pi_is_3.14
Video Solution by TheBeautyofMath
https://youtu.be/FV9AnyERgJQ?t=284
~IceMatrix
Video Solution by Interstigation
~Interstigation
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
