1988 AMC 12 Problem 3

Attempt Problem 3 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).

3.

Four rectangular paper strips of length 1010 and width 11 are put flat on a table and overlap perpendicularly as shown. How much area of the table is covered?
3636
4040
4444
9898
100100
Answer: A
Concepts:areainclusion-exclusionrectangles
Small hint:
First add the areas of the four strips
Big hint:
Each perpendicular crossing is a unit square counted twice
Solution:
The strips have total area 4(10)=40.4(10)=40. There are four 11-by-11 overlaps, each counted twice, so the covered area is 40−4=36.40-4=36.
Thus the correct answer is A.
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