Difference between revisions of "2021 AMC 10B Problems/Problem 17"
| Line 1: | Line 1: | ||
| − | + | ==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 <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--11, Oscar--4, Aditi--7, Tyrone--16, Kim--17. Which of the following statements is true? | ||
| + | |||
| + | <math> \textbf{(A) \ }\text{Ravon was given card 3.} \qquad \textbf{(B) \ }\text{Aditi was given card 3.} \qquad \textbf{(C) \ }\text{Ravon was given card 4.} \qquad \textbf{(D) \ }\text{Aditi was given card 4} \qquad </math> <math> \textbf{(E) \ }\text{Tyrone was givencard 7} </math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | Oscar must be given 3 and 1, so we rule out <math>\textbf{(A) \ }</math> and <math>\textbf{(B) \ }</math>. If Tyrone had card 7, then he would also have card 9, and then Kim must have 10 and 7 so we rule out <math>\textbf{(E) \ }</math>. If Aditi was given card 4, then she would have card 3, which Oscar already had. So the answer is <math>\boxed{\qquad \textbf{(C) \ }\text{Ravon was given card 4.}}</math> | ||
Revision as of 17:52, 11 February 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 
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?
Solution
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 
