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What is the % change in the area of a rectangle when its len

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What is the % change in the area of a rectangle when its len [#permalink] New post 06 Oct 2010, 05:09
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Question Stats:

60% (01:08) correct 40% (00:00) wrong based on 20 sessions
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data
[Reveal] Spoiler: OA
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Re: What is the % change in the area of a rectangle...... [#permalink] New post 06 Oct 2010, 05:24
Expert's post
pzazz12 wrote:
What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data


General formula for percent increase or decrease, (percent change):

Percent \ change=\frac{Change}{Original}*100.

area_{original}=lw and area_{new}=1.1l*0.9w=0.99lw --> Percent \ change=\frac{Change}{Original}*100=\frac{lw-0.99lw}{lw}*100=1% decrease.

Answer: D.
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Re: What is the % change in the area of a rectangle...... [#permalink] New post 12 Oct 2010, 12:16
Substitute if you don't know the formula.

First "rectangle" can be 10x10 so area is 100
Increase length by 10% and decrease width by 10% so 11x9 area is 99

100-99=1 sqft

1sqft is a 1% change from a 100 sqft rectangle.
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Re: What is the % change in the area of a rectangle...... [#permalink] New post 12 Oct 2010, 13:55
(11/10)*(9/10) = 99/100 of original area

99/100 is a 1% decrease from 100/100 ->D
Re: What is the % change in the area of a rectangle......   [#permalink] 12 Oct 2010, 13:55
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