Difference between revisions of "2008 AMC 8 Problems/Problem 9"

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==Problem==
 
==Problem==
In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During the the first year
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In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During the first year
 
her investment suffered a <math>15\%</math> loss, but during the second year the remaining
 
her investment suffered a <math>15\%</math> loss, but during the second year the remaining
 
investment showed a <math>20\%</math> gain. Over the two-year period, what was the change
 
investment showed a <math>20\%</math> gain. Over the two-year period, what was the change
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==See Also==
 
==See Also==
 
{{AMC8 box|year=2008|num-b=8|num-a=10}}
 
{{AMC8 box|year=2008|num-b=8|num-a=10}}
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{{MAA Notice}}

Revision as of 20:51, 7 February 2018

Problem

In $2005$ Tycoon Tammy invested $100$ dollars for two years. During the first year her investment suffered a $15\%$ loss, but during the second year the remaining investment showed a $20\%$ gain. Over the two-year period, what was the change in Tammy's investment?

$\textbf{(A)}\  5\%\text{ loss}\qquad \textbf{(B)}\ 2\%\text{ loss}\qquad \textbf{(C)}\ 1\%\text{ gain}\qquad \textbf{(D)}\ 2\% \text{ gain} \qquad \textbf{(E)}\  5\%\text{ gain}$

Solution

After the $15 \%$ loss, Tammy has $100 \cdot 0.85 = 85$ dollars. After the $20 \%$ gain, she has $85 \cdot 1.2 = 102$ dollars. This is an increase in $2$ dollars from her original $100$ dollars, a $\boxed{\textbf{(D)}\ 2 \%\ \text{gain}}$.

See Also

2008 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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 AJHSME/AMC 8 Problems and Solutions

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