AMC10 2021 B

AMC10 2021 B · Q17

AMC10 2021 B · Q17. It mainly tests Casework, Logic puzzles.

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、Oscar、Aditi、Tyrone 和 Kim 玩一个纸牌游戏。每人从编号为 $1,2,3, \dots,10$ 的 $10$ 张牌中获得 $2$ 张牌。玩家的得分是他们牌上数字之和。玩家的得分为：Ravon--$11,$ Oscar--$4,$ Aditi--$7,$ Tyrone--$16,$ Kim--$17$。以下哪个陈述是正确的？

(A) \text{Ravon was given card 3.} \text{Ravon was given card 3.}

(B) \text{Aditi was given card 3.} \text{Aditi was given card 3.}

(D) \text{Aditi was given card 4.} \text{Aditi was given card 4.}

(E) \text{Tyrone was given card 7.} \text{Tyrone was given card 7.}

Answer

Correct choice: (C)

正确答案：（C）

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 $\textbf{(C)}.$

通过逻辑推导，我们按得分从低到高考虑： \begin{align*} \text{Oscar 的得分是 4.} &\implies \text{Oscar 拿到牌 1 和 3.} \\ &\implies \text{Aditi 拿到牌 2 和 5.} \\ &\implies \text{Ravon 拿到牌 4 和 7.} && (\bigstar) \\ &\implies \text{Tyrone 拿到牌 6 和 10.} \\ &\implies \text{Kim 拿到牌 8 和 9.} \end{align*} 因此，答案是 $\boxed{\textbf{(C) }\text{Ravon 拿到了牌 4}}$。当然，如果我们先阅读答案选项，那么可以在 $(\bigstar)$ 处停止并选择 $\textbf{(C)}$。

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