2012 AMC 12B Problem 4

Attempt Problem 4 of the 2012 AMC 12B 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 2012 AMC 12B solutions, or check the answer key.

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

Suppose that the euro is worth $1.30$ dollars. If Diana has $500$ dollars and Étienne has $400$ euros, by what percent is the value of Étienne's money greater than the value of Diana's money?

$2$

$4$

$6.5$

$8$

$13$

Answer: B

Concepts:percentage unit conversion

Difficulty rating: 1050

Solution:

Étienne's money is worth $400\cdot1.30=520$ dollars, while Diana has $500$ dollars.

The percent by which Étienne's value exceeds Diana's is $\frac{520-500}{500}\cdot100\%=4\%.$

Thus, the correct answer is B.

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