1952 AMC 12 Problem 20

Attempt Problem 20 of the 1952 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 1952 AMC 12 solutions, or check the answer key.

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20.

\dfrac xy=\dfrac34,

then the incorrect expression in the following is:

\dfrac{x+y}{y}=\dfrac74

\dfrac{y}{y-x}=\dfrac41

\dfrac{x+2y}{x}=\dfrac{11}3

\dfrac{x}{2y}=\dfrac38

\dfrac{x-y}{y}=\dfrac14

Let

x=3k

and

y=4k

Pay attention to the sign of

x-y

Set

x=3k

and

y=4k.

The first four expressions become

\frac{7}{4},

4,

\frac{11}{3},

and

\frac{3}{8},

respectively. But

\frac{x-y}{y}=\frac{3k-4k}{4k}=-\frac14,

not

\frac{1}{4}.

Thus, the correct answer is E.

Problem 20 in other years