AMC10 2007 A

AMC10 2007 A · Q6

AMC10 2007 A · Q6. It mainly tests Percent, Averages (mean).

At Euclid High School, the number of students taking the AMC10 was $60$ in $2002$, $66$ in $2003$, $70$ in $2004$, $76$ in $2005$, and $78$ in $2006$, and is $85$ in $2007$. Between what two consecutive years was there the largest percentage increase?

在Euclid高中，参加AMC10的学生人数2002年为$60$人，2003年为$66$人，2004年为$70$人，2005年为$76$人，2006年为$78$人，2007年为$85$人。哪两个连续年份之间的百分比增长最大？

(A) 2002 and 2003 2002和2003

(B) 2003 and 2004 2003和2004

(D) 2005 and 2006 2005和2006

(E) 2006 and 2007 2006和2007

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): Between 2002 and 2003, the increase was \[ \frac{6}{60}=\frac{1}{10}=10\%. \] Between the other four pairs of consecutive years, the increases were \[ \frac{4}{66}<\frac{4}{40}=\frac{1}{10},\quad \frac{6}{70}<\frac{6}{60}=\frac{1}{10},\quad \frac{2}{76}<\frac{2}{20}=\frac{1}{10},\quad \text{and}\quad \frac{7}{78}<\frac{7}{70}=\frac{1}{10}. \] Therefore the largest percentage increase occurred between 2002 and 2003.

答案（A）：在2002年到2003年之间，增幅为 \[ \frac{6}{60}=\frac{1}{10}=10\%. \] 在其余四对相邻年份之间，增幅为 \[ \frac{4}{66}<\frac{4}{40}=\frac{1}{10},\quad \frac{6}{70}<\frac{6}{60}=\frac{1}{10},\quad \frac{2}{76}<\frac{2}{20}=\frac{1}{10},\quad \text{并且}\quad \frac{7}{78}<\frac{7}{70}=\frac{1}{10}. \] 因此，最大的百分比增幅发生在2002年到2003年之间。

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