Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(All solutions to this problem are incredibly similar (repetitive). So, I cleaned up this page by keeping a comprehensive solution. I will give credit to all users who ever contributed to the written solutions. Let me know if you are unhappy with this edit)
m (→‎Video Solution by OmegaLearn (Using logical deduction))
Line 28: Line 28:
 
~smarty101 ~smartypantsno_3 ~SmileKat32 ~MRENTHUSIASM
 
~smarty101 ~smartypantsno_3 ~SmileKat32 ~MRENTHUSIASM
  
−
== Video Solution by OmegaLearn (Using logical deduction) ==
+
== Video Solution by OmegaLearn (Using Logical Deduction) ==
 
https://youtu.be/zO0EuKPXuT0
 
https://youtu.be/zO0EuKPXuT0
  

Revision as of 21:21, 7 September 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 observations, we consider the scores from lowest to highest. We make the following logical deduction: \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 (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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_AMC_10B_Problems/Problem_17&oldid=161837"