GMAT
题目
Jamal gets three monthly credit card statements over the course of three months. If his average monthly statement over these three months is $44 more than the median amount, and the sum of the largest and the smallest statement is $412, what is the total amount that Jamal spent over these three months?
解析
设3个月的支出分别为\( A \)、\( B \)、\( C \)，满足\( A ≤ B ≤ C \)。
因此**中位数**\( = B \)。
已知月均支出比中位数多44美元，
即：\( \frac{A+B+C}{3} = 44 + B \)
同时已知\( A + C = 412 \)，将其代入上式：
\[
\begin{align*}
\frac{412+B}{3} &= 44 + B \\
412 + B &= 132 + 3B \\
280 &= 2B \\
B &= 140
\end{align*}
\]
因此总支出\( = A + B + C = 412 + 140 = 552 \)。
正确答案是选项B。
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