1954 AMC 12 Problem 3

Attempt Problem 3 of the 1954 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 1954 AMC 12 solutions, or check the answer key.

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

x

varies as the cube of

y,

and

y

varies as the fifth root of

z,

then

x

varies as the

n

th power of

z,

where

n

is:

\dfrac1{15}

\dfrac53

\dfrac35

15

8

Write

x=k_1y^3

and

y=k_2z^{\frac{1}{5}}

Substitute the second variation law into the first and multiply the exponents

Since

y

is proportional to

z^{\frac{1}{5}},

its cube is proportional to

z^{\frac{3}{5}}.

Because

x

is proportional to

y^3,

x\propto z^{\frac{3}{5}}.

Hence

n=\frac{3}{5}.

Thus, the correct answer is C.

Problem 3 in other years