1953 AMC 12 Problem 19

Attempt Problem 19 of the 1953 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 1953 AMC 12 solutions, or check the answer key.

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19.

In the expression

xy^2,

the values of

x

and

y

are each decreased

25\%;

the value of the expression is:

decreased

50\%

decreased

75\%

decreased

\frac{37}{64}

of its value

decreased

\frac{27}{64}

of its value

none of these

Each decreased variable is

\frac{3}{4}

of its original value

Account for the two powers of

y

when finding the new multiplicative factor

The new value is

\left(\frac34x\right)\left(\frac34y\right)^2 =\frac{27}{64}xy^2.

Therefore the decrease is

1-\frac{27}{64}=\frac{37}{64}

of the original value.

Thus, the correct answer is C.

Problem 19 in other years