During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

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

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

~ pi_is_3.14

~IceMatrix

Video Solution by Interstigation

~Interstigation

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 