1988 AMC 12 Problem 11

Attempt Problem 11 of the 1988 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 1988 AMC 12 solutions, or check the answer key.

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

11.

On each horizontal line in the figure below, the five large dots indicate the populations of cities

A,

B,

C,

D,

and

E

in the year indicated. Which city had the greatest percentage increase in population from

1970

1980?

A

B

C

D

E

Read each city’s two population values from the scale

Compare increase divided by the

1970

population, not just absolute increase

The percentage increases for

A,B,C,D,E

are respectively

\frac{10}{40},\frac{20}{50},\frac{30}{70},\frac{30}{100},

and

\frac{40}{120}.

These are

25\%,40\%,42\frac67\%,30\%,

and

33\frac13\%,

so city

C

has the greatest percentage increase.

Thus the correct answer is C.

Problem 11 in other years