2012 AMC 12A Problem 3

Attempt Problem 3 of the 2012 AMC 12A 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 12A solutions, or check the answer key.

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

A box $2$ centimeters high, $3$ centimeters wide, and $5$ centimeters long can hold $40$ grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold $n$ grams of clay. What is $n?$

$120$

$160$

$200$

$240$

$280$

Answer: D

Concepts:volume ratio and proportion

Difficulty rating: 880

Solution:

The second box has $2 \times 3 \times 1 = 6$ times the volume of the first, so it holds $6$ times as much clay.

Therefore $n = 6 \cdot 40 = 240.$

Thus, the correct answer is D.

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