Given two positive integers x and y with x< y. The percent that x is less than y is:

1956 AMC 12 Problem 13

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13.

Given two positive integers

x

and

y

with

x\lt y.

The percent that

x

is less than

y

is:

\dfrac{100(y-x)}x

\dfrac{100(x-y)}x

\dfrac{100(y-x)}y

100(y-x)

100(x-y)

The amount by which

x

is smaller is

y-x

Because the comparison is to

y,

use

y

as the denominator

The difference is

y-x.

Measured as a fraction of the reference value

y,

this is

\frac{y-x}{y}.

Multiplying by

100

converts the fraction to a percent:

\frac{100(y-x)}y.

Thus, the correct answer is C.