2008 AMC 8 Problem 9

Attempt Problem 9 of the 2008 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

In 20052005 Tycoon Tammy invested $100\$100 for two years. During the first year her investment suffered a 15%15\% loss, but during the second year the remaining investment showed a 20%20\% gain. Over the two-year period, what was the change in Tammy’s investment?
5%5\% loss
2%2\% loss
1%1\% gain
2%2\% gain
5%5\% gain
Answer: D
Concepts:percentage
Small hint:
After a 15%15\% loss, 85%85\% of the original investment remains.
Big hint:
Apply the 20%20\% gain to the reduced amount, not to the original amount.
Solution:
The 15%15\% loss changes the investment from $100\$100 to 0.85⋅$100=$850.85\cdot\$100=\$85.
The 20%20\% gain then changes it to 1.2⋅$85=$1021.2\cdot\$85=\$102.
The investment went from $100\$100 to $102\$102, which is a 2%2\% gain.
Thus, D is the correct answer.
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