2009 AMC 12B Problem 7

Below is the professionally curated solution for Problem 7 of the 2009 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 12B solutions, or check the answer key.

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Concepts:percentage

Difficulty rating: 1330

In a certain year the price of gasoline rose by $20\%$ during January, fell by $20\%$ during February, rose by $25\%$ during March, and fell by $x\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x?$

$12$

$17$

$20$

$25$

$35$

Solution:

After January through March the price is $1.2 \cdot 0.8 \cdot 1.25 = 1.2$ times the original.

To return to the original, April must multiply by $\dfrac{1}{1.2},$ a decrease of $1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%.$ To the nearest integer, $x = 17.$

Thus, the correct answer is B.

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