# 2007 AMC 10A Problems/Problem 6

## Problem

At Euclid High School, the number of students taking the AMC 10 was $60$ in 2002, $66$ in 2003, $70$ in 2004, $76$ in 2005, $78$ and 2006, and is $85$ in 2007. Between what two consecutive years was there the largest percentage increase? $\text{(A)}\ 2002\ \text{and}\ 2003 \qquad \text{(B)}\ 2003\ \text{and}\ 2004 \qquad \text{(C)}\ 2004\ \text{and}\ 2005 \qquad \text{(D)}\ 2005\ \text{and}\ 2006 \qquad \text{(E)}\ 2006\ \text{and}\ 2007$

## Solution

We compute the percentage increases:

1. $\frac{66 - 60}{60} = 10\%$
2. $\frac{70 - 66}{66} \approx 6\%$
3. $\frac{76-70}{70} \approx 8.6\%$
4. $\frac{78-76}{76} \approx 2.6\%$
5. $\frac{85-78}{78} \approx 9\%$

The answer is $\mathrm{(A)}$.

In fact, the answer follows directly from examining the differences between each year. The largest differences are $6,6,7$, and it is easy to see that due to the decreased starting number of students in 2002 that that will be our answer.

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 