2012 AMC 12A Problem 3

Below is the professionally curated solution for Problem 3 of the 2012 AMC 12A, 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.

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Concepts:volume ratio and proportion

Difficulty rating: 880

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 $n?$

$120$

$160$

$200$

$240$

$280$

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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