1961 AMC 12 Problem 18

Attempt Problem 18 of the 1961 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 1961 AMC 12 solutions, or check the answer key.

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

18.

The yearly changes in the population census of a town for four consecutive years are, respectively,

25\%

increase,

25\%

increase,

25\%

decrease,

25\%

decrease. The net change over the four years, to the nearest percent, is:

-12

-1

0

1

12

Represent each increase by a factor of

1.25

and each decrease by

0.75

Compare

1.25^2\cdot0.75^2

with

1

The final population is multiplied by

(1.25)^2(0.75)^2=\frac{225}{256}\approx0.879.

This is a decrease of about

12.1\%,

which rounds to

12\%.

Thus, the correct answer is A.

Problem 18 in other years