Question

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?

Ravon was given card 3.

Aditi was given card 3.

Ravon was given card 4.

Aditi was given card 4.

Tyrone was given card 7.

Video solution:

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Written solution:

If there are $2$ cards for Oscar that add up to $4,$ he must have both $1$ and $3.$ This eliminates choices A and B.

If there are $2$ cards for Aditi that add up to $7,$ he must have both $2$ and $5$ so she doesn't have $1$ and $3.$

If someone has $4,$ their sum must be equal to or under $14$ since the other number must be under or equal to $10.$ Thus, Ravon must have the $4$ and $7,$ making C true and D and E false.

Thus, the answer is C .

2021 AMC 10B Spring Problem 17

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Written solution:

Problem 17 in Other Years