AMC10 2021 A

AMC10 2021 A · Q7

AMC10 2021 A · Q7. It mainly tests Logic puzzles.

Tom has a collection of $13$ snakes, $4$ of which are purple and $5$ of which are happy. He observes that Which of these conclusions can be drawn about Tom's snakes?

Tom 有 13 条蛇，其中 4 条是紫色的，5 条是快乐的。他观察到关于 Tom 的蛇，可以得出以下哪项结论？

(A) Purple snakes can add. $ Purple snakes can add.

(B) Purple snakes are happy. $ Purple snakes are happy.

(D) Happy snakes are not purple. $ Happy snakes are not purple.

(E) Happy snakes can't subtract. $ Happy snakes can't subtract.

Answer

Correct choice: (D)

正确答案：（D）

Solution

To see that choices (A), (B), (C), and (E) do not follow from the given information, consider the following two snakes that may be part of Tom's collection. One snake is happy but not purple and can both add and subtract. The second is purple but not happy and can neither add nor subtract. Then each of the three bulleted statements is true, but each of these choices is false. To show that answer choice (D) is correct, first observe that the third bulleted statement is equivalent to "Snakes that can add also can subtract." The second bulleted statement is equivalent to "Snakes that can subtract are not purple." The three bulleted statements combined then lead to the conclusion (D) Happy snakes are not purple.

为了说明选项 (A)、(B)、(C) 和 (E) 不能从已知信息推出，考虑下面两条可能属于汤姆收藏的蛇。一条蛇是快乐的但不是紫色的，并且既能加也能减。第二条蛇是紫色的但不快乐，并且既不能加也不能减。这样，三个项目符号陈述都为真，但这些选项各自都是假的。为了证明答案选项 (D) 正确，先注意第三个项目符号陈述等价于“能加的蛇也能减”。第二个项目符号陈述等价于“能减的蛇不是紫色的”。将这三个项目符号陈述合在一起，就得到结论 (D)：快乐的蛇不是紫色的。

Topics

LM.001 Logic puzzles