2018 AMC 12A Problem 1

Attempt Problem 1 of the 2018 AMC 12A 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 2018 AMC 12A solutions, or check the answer key.

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

A large urn contains

100

balls, of which

36\%

are red and the rest are blue. How many of the blue balls must be removed so that the percentage of red balls in the urn will be

72\%?

(No red balls are to be removed.)

28

32

36

50

64

The number of red balls never changes; only blue balls leave

36

red balls are to be

72\%

of the urn, the urn must hold

36 \div 0.72

balls

There are

36

red balls, and this count stays fixed. For the red balls to be

72\%

of the urn, the urn must contain

36 \div 0.72 = 50

balls. Since

100 - 50 = 50

, exactly

50

blue balls are removed.

Thus, the correct answer is D.

Problem 1 in other years