1955 AMC 12 Problem 5

Attempt Problem 5 of the 1955 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 1955 AMC 12 solutions, or check the answer key.

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

y

varies inversely as the square of

x.

When

y=16,

x=1.

When

x=8,

y

equals:

2

128

64

\dfrac14

1024

Write the variation as

y=\frac{k}{x^2}

Use the first pair of values to determine

k

Inverse-square variation gives

y=\frac{k}{x^2}.

Since

16=\frac{k}{1^2},

we have

k=16.

x=8,

y=\frac{16}{8^2}=\frac14.

Thus, the correct answer is D.

Problem 5 in other years