1993 AMC 8 Problem 21

Attempt Problem 21 of the 1993 AMC 8 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 1993 AMC 8 solutions, or check the answer key.

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

21.

If the length of a rectangle is increased by 20%20\% and its width is increased by 50%,50\%, then the area is increased by
10%10\%
30%30\%
70%70\%
80%80\%
100%100\%
Answer: D
Concepts:percentage
Small hint:
New area == (new length) ×\times (new width) =1.2×1.5= 1.2 \times 1.5 times the old area
Big hint:
Multiply the two growth factors 1.21.2 and 1.51.5 to get the factor by which the area grows
Solution:
The new length is 1.21.2 times the old and the new width is 1.51.5 times the old, so the new area is 1.2×1.5=1.81.2 \times 1.5 = 1.8 times the old area.
That is an increase of 80%.80\%.
Thus, the correct answer is D .
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