Question

Ravon、Oscar、Aditi、Tyrone 和 Kim 玩一个纸牌游戏。每人从编号 $1,2,3, \dots,10$ 的 $10$ 张牌中拿到 $2$ 张。玩家的得分是自己两张牌上数字之和。五人的得分如下：Ravon 为 $11$ ，Oscar 为 $4$ ，Aditi 为 $7$ ，Tyrone 为 $16$ ，Kim 为 $17$ 。下列哪项陈述正确？

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 拿到了 3 号牌。

Ravon was given card 3.

Aditi 拿到了 3 号牌。

Aditi was given card 3.

Ravon 拿到了 4 号牌。

Ravon was given card 4.

Aditi 拿到了 4 号牌。

Aditi was given card 4.

Tyrone 拿到了 7 号牌。

Tyrone was given card 7.

答案：C

知识点：逻辑推理

难度评级：1420

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文字解答：

Oscar 的得分为 $4$ ，所以他的牌必须是 $1$ 和 $3.$ 在剩余牌中，和为 $7$ 的唯一一对是 $2$ 和 $5,$ 所以它们是 Aditi 的牌。

未使用的牌是 $4,6,7,8,9,10.$ Tyrone 的得分 $16$ 只能来自 $6+10$ 或 $7+9.$ 若 Tyrone 拿到 $7$ 和 $9,$ 剩余的 $4,6,8,10$ 无法配成 Ravon 的得分 $11.$ 因此 Tyrone 拿到 $6$ 和 $10.$

剩余的牌是 $4,7,8,9.$ Ravon 必须拿 $4$ 和 $7$ ，得分才为 $11,$ 留下 $8$ 和 $9$ 给 Kim，得分为 $17.$ 所以 Ravon 拿到了 $4.$ 号牌。

所以答案是 C。

Oscar's score of $4$ forces his cards to be $1$ and $3.$ From the remaining cards, the only pair with sum $7$ is $2$ and $5,$ so those are Aditi's cards.

The unused cards are now $4,6,7,8,9,10.$ Tyrone's score of $16$ can come only from $6+10$ or $7+9.$ If Tyrone had $7$ and $9,$ then the remaining cards $4,6,8,10$ could not be paired to give Ravon's score $11.$ Thus Tyrone has $6$ and $10.$

The remaining cards are $4,7,8,9.$ Ravon must have $4$ and $7$ to score $11,$ leaving $8$ and $9$ for Kim's score of $17.$ Therefore, Ravon was given card $4.$

Thus, the answer is C .

2021 AMC 10B Spring 第 17 题

答案：C

难度评级：1420

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