AMC8 2002

AMC8 2002 · Q17

AMC8 2002 · Q17. It mainly tests Linear equations, Arithmetic misc.

In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?

在一场有十道题的数学竞赛中，学生答对一题得5分，答错一题扣2分。如果Olivia回答了所有题目，她的得分为29，她答对了几题？

(A) 5 5

(B) 6 6

(D) 8 8

(E) 9 9

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) Olivia solved at least 6 correctly to have scored over 25. Her score for six correct would be $6(+5)+4(-2)=22$, which is too low. If she answered 7 correctly, her score would be $7(+5)+3(-2)=29$, and this was her score. The correct choice is (C).

（C）Olivia 至少答对了 6 题才能得分超过 25。她若答对 6 题，得分为 $6(+5)+4(-2)=22$，这太低了。如果她答对 7 题，得分为 $7(+5)+3(-2)=29$，而这正是她的得分。正确选项是（C）。

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