AMC12 2005 B

AMC12 2005 B · Q4

AMC12 2005 B · Q4. It mainly tests Percent, Rounding & estimation.

At the beginning of the school year, Lisa's goal was to earn an $A$ on at least $80\%$ of her $50$ quizzes for the year. She earned an $A$ on $22$ of the first $30$ quizzes. If she is to achieve her goal, on at most how many of the remaining quizzes can she earn a grade lower than an $A$?

在学年开始时，丽莎的目标是在全年$50$次小测验中至少有$80\%$获得$A$。她在前$30$次小测验中有$22$次获得$A$。如果她要实现目标，那么在剩下的小测验中，最多有多少次她可以得到低于$A$的成绩？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

Lisa's goal was to get an $A$ on $80\% \cdot 50 = 40$ quizzes. She already has $A$'s on $22$ quizzes, so she needs to get $A$'s on $40-22=18$ more. There are $50-30=20$ quizzes left, so she can afford to get less than an $A$ on $20-18=\boxed{\textbf{(B) }2}$ of them. Here, only the $A$'s matter... No complicated stuff!

丽莎的目标是在 $80\% \cdot 50 = 40$ 次小测验中获得 $A$。她已经在 $22$ 次小测验中获得了 $A$，所以她还需要再获得 $40-22=18$ 个 $A$。还剩下 $50-30=20$ 次小测验，因此她最多可以在其中 $20-18=\boxed{\textbf{(B) }2}$ 次得到低于 $A$ 的成绩。这里，只有获得 $A$ 的次数重要……不需要复杂的东西！

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