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# If the length of a rectangle is increased by 20 percent and the width

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Math Expert
Joined: 02 Sep 2009
Posts: 42606

Kudos [?]: 135614 [0], given: 12705

If the length of a rectangle is increased by 20 percent and the width [#permalink]

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16 Oct 2017, 08:53
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Difficulty:

5% (low)

Question Stats:

100% (00:39) correct 0% (00:00) wrong based on 60 sessions

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If the length of a rectangle is increased by 20 percent and the width is decreased by 20 percent, then the area

(A) decreases by 20%
(B) decreases by 4%
(C) stays the same
(D) increases by 10%
(E) increases by 20%
[Reveal] Spoiler: OA

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Kudos [?]: 135614 [0], given: 12705

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [0], given: 645

If the length of a rectangle is increased by 20 percent and the width [#permalink]

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16 Oct 2017, 11:34
Bunuel wrote:
If the length of a rectangle is increased by 20 percent and the width is decreased by 20 percent, then the area

(A) decreases by 20%
(B) decreases by 4%
(C) stays the same
(D) increases by 10%
(E) increases by 20%

Assign values
Let L = 10
Let W = 10 (a square is a rectangle)

Original area = (LW) = 10*10 = 100

L increases by 20 percent:
(1.2)(10) = 12

W decreases by 20 percent:
(0.8)(10) = 8

New area: (12)*(8) = 96

Percent change:$$\frac{New-Old}{Old} * 100$$

$$\frac{96-100}{100}=$$
$$(-.04) * 100$$ = 4 percent decrease

Algebra
L = length
W = width
Area = (1)LW

Length increases by 20 percent, width decreases by 20 percent:

1.2L * 0.8W = (.96) LW

.96 is 4 percent less than 1

The area decreases by 4 percent

Kudos [?]: 402 [0], given: 645

Manager
Joined: 09 Aug 2017
Posts: 59

Kudos [?]: 8 [0], given: 18

Location: United States
Concentration: Technology
GMAT 1: 640 Q44 V33
GMAT 2: 630 Q47 V29
WE: Research (Investment Banking)
If the length of a rectangle is increased by 20 percent and the width [#permalink]

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23 Oct 2017, 06:02
One thing I try to remind myself is that squares are rectangles.
-So I started with a square with sides of 5, area would equal 25. I chose 5 as the size of the sides because it's easy to increase and decrease by 20%.
-Length is increased by 20% 5+1=6.
-Width is decreased by 20%, 5-1=4
-New area is 4*6=24.
-(24-25)/25=-1/25=-4%.

-My biggest problem is dumb mistakes, if positive 4% was an answer, I might have chosen it. If anyone has any advice on dumb mistakes, please share.
_________________

I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

Also, I appreciate any kudos.

Kudos [?]: 8 [0], given: 18

VP
Joined: 22 May 2016
Posts: 1126

Kudos [?]: 402 [1], given: 645

If the length of a rectangle is increased by 20 percent and the width [#permalink]

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23 Oct 2017, 08:41
1
KUDOS
Plunkster82 wrote:
One thing I try to remind myself is that squares are rectangles.
-So I started with a square with sides of 5, area would equal 25. I chose 5 as the size of the sides because it's easy to increase and decrease by 20%.
-Length is increased by 20% 5+1=6.
-Width is decreased by 20%, 5-1=4
-New area is 4*6=24.
-(24-25)/25=-1/25=-4%.

-My biggest problem is dumb mistakes, if positive 4% was an answer, I might have chosen it. If anyone has any advice on dumb mistakes, please share.

My two cents':

1) check your answers. On this kind of question, try different numbers. The square as rectangle is a great idea. But with percentages, try to use values such as 10 and 100 that give you a base of 100. Try 10 here as original L and W. You'll get 96 vs 100: Four percent smaller.

2) write down all but the most simple things, neatly. One of my favorite experts at gmatclub is a fan of mental math. I am not.

Tip of the Week, posts from Brian Galvin at Veritas Prep and great links from Bunuel: HERE

Another, HERE

Another, HERE

After those, I would run two Google searches with these terms:
1) GMAT dumb silly mistakes gmatclub; and
2) same, but omit "gmatclub"

Hope it helps.

Kudos [?]: 402 [1], given: 645

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1802

Kudos [?]: 981 [0], given: 5

Re: If the length of a rectangle is increased by 20 percent and the width [#permalink]

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26 Oct 2017, 09:44
Bunuel wrote:
If the length of a rectangle is increased by 20 percent and the width is decreased by 20 percent, then the area

(A) decreases by 20%
(B) decreases by 4%
(C) stays the same
(D) increases by 10%
(E) increases by 20%

We can let L = the original length and W = the original width; thus, the original area of the rectangle is LW and the new area is 1.2L x 0.8W = 0.96LW, so the area is decreased by 4%.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [0], given: 5

Re: If the length of a rectangle is increased by 20 percent and the width   [#permalink] 26 Oct 2017, 09:44
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