Difference between revisions of "2021 AMC 10B Problems/Problem 17"

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i dont know the questions
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==Problem==
but i know ur tryna see them
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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?
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<math>\textbf{(A) }\text{Ravon was given card 3.}</math>
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<math>\textbf{(B) }\text{Aditi was given card 3.}</math>
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<math>\textbf{(C) }\text{Ravon was given card 4.}</math>
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<math>\textbf{(D) }\text{Aditi was given card 4.}</math>
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<math>\textbf{(E) }\text{Tyrone was given card 7.}</math>
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==Solution==
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By logical deduction, we consider the scores from lowest to highest:
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<cmath>\begin{align*}
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\text{Oscar's score is 4.} &\implies \text{Oscar is given cards 1 and 3.} \\
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&\implies \text{Aditi is given cards 2 and 5.} \\
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&\implies \text{Ravon is given cards 4 and 7.} && (\bigstar) \\
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&\implies \text{Tyrone is given cards 6 and 10.} \\
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&\implies \text{Kim is given cards 8 and 9.}
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\end{align*}</cmath>
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Therefore, the answer is <math>\boxed{\textbf{(C) }\text{Ravon was given card 4.}}</math>
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Certainly, if we read the answer choices sooner, then we can stop at <math>(\bigstar)</math> and pick <math>\textbf{(C)}.</math>
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~smarty101 ~smartypantsno_3 ~SmileKat32 ~MRENTHUSIASM
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== Video Solution by OmegaLearn (Using Logical Deduction) ==
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https://youtu.be/zO0EuKPXuT0
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~ pi_is_3.14
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==Video Solution by TheBeautyofMath==
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https://youtu.be/FV9AnyERgJQ?t=284
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~IceMatrix
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==Video Solution by Interstigation==
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https://youtu.be/8BPKs24eyes
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~Interstigation
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==See Also==
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{{AMC10 box|year=2021|ab=B|num-b=16|num-a=18}}
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{{MAA Notice}}

Latest revision as of 16:18, 6 November 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 $1,2,3, \dots,10.$ 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?

$\textbf{(A) }\text{Ravon was given card 3.}$

$\textbf{(B) }\text{Aditi was given card 3.}$

$\textbf{(C) }\text{Ravon was given card 4.}$

$\textbf{(D) }\text{Aditi was given card 4.}$

$\textbf{(E) }\text{Tyrone was given card 7.}$

Solution

By logical deduction, we consider the scores from lowest to highest: \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*} Therefore, the answer is $\boxed{\textbf{(C) }\text{Ravon was given card 4.}}$

Certainly, if we read the answer choices sooner, then we can stop at $(\bigstar)$ and pick $\textbf{(C)}.$

~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

2021 AMC 10B (ProblemsAnswer KeyResources)
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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