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

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Manager
Joined: 22 Sep 2010
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What is the % change in the area of a rectangle when its len [#permalink]  06 Oct 2010, 05:09
00:00

Difficulty:

15% (low)

Question Stats:

66% (01:18) correct 34% (00:07) wrong based on 38 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
Math Expert
Joined: 02 Sep 2009
Posts: 28348
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Re: What is the % change in the area of a rectangle...... [#permalink]  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.

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Intern
Joined: 12 Oct 2010
Posts: 15
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Kudos [?]: 3 [0], given: 11

Re: What is the % change in the area of a rectangle...... [#permalink]  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.
Intern
Joined: 24 Jun 2010
Posts: 41
Location: Toronto
Schools: Berkeley Haas, UCLA Anderson, NYU Stern
Followers: 1

Kudos [?]: 6 [0], given: 3

Re: What is the % change in the area of a rectangle...... [#permalink]  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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