Difference between revisions of "2007 AMC 10A Problems/Problem 6"
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<math>\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</math> | <math>\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</math> | ||
| − | == Solution == | + | == Solution 1 == |
We compute the percentage increases: | We compute the percentage increases: | ||
| Line 15: | Line 15: | ||
The answer is <math>\mathrm{(A)}</math>. | The answer is <math>\mathrm{(A)}</math>. | ||
| − | In fact, the answer follows directly from examining the differences between each year. The largest differences are <math>6 | + | In fact, the answer follows directly from examining the differences between each year. The largest differences are <math>6</math> and <math>7</math>. Due to the decreased starting number of students between <math>2002</math> and <math>2003</math>, that interval will be our answer. |
| + | |||
| + | ~edited by mobius247 | ||
| + | |||
| + | == Solution 2 == | ||
| + | |||
| + | We make the numerator 1 and compare the denominators. | ||
| + | |||
| + | #<math>\frac{66 - 60}{60} = \frac{1}{10}</math> | ||
| + | |||
| + | #<math>\frac{70 - 66}{66} = \frac{1}{16.5}</math> | ||
| + | |||
| + | #<math>\frac{76-70}{70} \approx \frac{1}{11.7}</math> | ||
| + | |||
| + | #<math>\frac{78-76}{76} = \frac{1}{38}</math> | ||
| + | |||
| + | #<math>\frac{85-78}{78} \approx \frac{1}{11.1}</math> | ||
| + | |||
| + | |||
| + | The answer is <math>\mathrm{(A)}</math>. | ||
| + | |||
| + | ~thatmathsguy | ||
== See also == | == See also == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:55, 2 June 2023
Contents
Problem
At Euclid High School, the number of students taking the AMC 10 was 
in 2002, 
in 2003, 
in 2004, 
in 2005, 
and 2006, and is 
in 2007. Between what two consecutive years was there the largest percentage increase?
Solution 1
We compute the percentage increases:
The answer is 
.
In fact, the answer follows directly from examining the differences between each year. The largest differences are 
and 
. Due to the decreased starting number of students between 
and 
, that interval will be our answer.
~edited by mobius247
Solution 2
We make the numerator 1 and compare the denominators.
The answer is .
~thatmathsguy
See also
| 2007 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 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. 
