If a is 50% larger than c, and b is 25% larger than c, then a is what percent larger than b?

1997 AMC 12 Problem 4

Attempt Problem 4 of the 1997 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 1997 AMC 12 solutions, or check the answer key.

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a

50\%

larger than

c,

and

b

25\%

larger than

c,

then

a

is what percent larger than

b?

20\%

25\%

50\%

100\%

200\%

Write both

a

and

b

as multiples of

c

The requested percentage uses

b

, not

c

, as its base

We have

a=1.5c

and

b=1.25c.

Thus

\frac{a}{b}=\frac{1.5}{1.25}=1.2,

a

20\%

larger than

b.

The correct answer is A.