1961 AMC 12 Problem 15

Attempt Problem 15 of the 1961 AMC 12 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 1961 AMC 12 solutions, or check the answer key.

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15.

x

men working

x

hours a day for

x

days produce

x

articles, then the number of articles (not necessarily an integer) produced by

y

men working

y

hours a day for

y

days is:

\dfrac{x^3}{y^2}

\dfrac{y^3}{x^2}

\dfrac{x^2}{y^3}

\dfrac{y^2}{x^3}

y

Compute the production per man-hour from the first situation

The second situation uses

y^3

man-hours

The first group uses

x^3

man-hours to make

x

articles, so the rate is

\frac{1}{x^2}

article per man-hour. The second group supplies

y^3

man-hours and therefore makes

\frac{y^3}{x^2}

articles.

Thus, the correct answer is B.

Problem 15 in other years