# Difference between revisions of "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 $6$ and $7$. Due to the decreased starting number of students between 2002 and 2003, that year will be our answer.

## See also

 2007 AMC 10A (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions

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

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