1959 AMC 12 Problem 20

Attempt Problem 20 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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

20.

It is given that

x

varies directly as

y

and inversely as the square of

z,

and that

x=10

when

y=4

and

z=14.

Then, when

y=16

and

z=7,

x

equals:

180

160

154

140

120

Write

x=\frac{ky}{z^2}

Compare the new and old values by ratios so the constant cancels

Because

x=\frac{ky}{z^2},

\frac{x_{\rm new}}{10} =\frac{16}{4}\left(\frac{14}{7}\right)^2 =4\cdot4=16.

Hence

x_{\rm new}=160.

Thus, the correct answer is B.

Problem 20 in other years