1995 AMC 12 Problem 5

Attempt Problem 5 of the 1995 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 1995 AMC 12 solutions, or check the answer key.

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

A rectangular field is

300

feet wide and

400

feet long. Random sampling indicates that there are, on the average, three ants per square inch throughout the field. [

12

inches =

1

foot.] Of the following, the number that most closely approximates the number of ants in the field is

500

thousand

5

million

50

million

500

million

5

billion

First find the field’s area in square feet

One square foot contains

12^2

square inches

The area is

300\cdot400=120{,}000

square feet, or

120{,}000\cdot144=17{,}280{,}000

square inches. The estimate is

3(17{,}280{,}000)=51{,}840{,}000,

closest to

50

million. Thus the correct answer is C.

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