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In a rectangle, the length is increased by 10%, and the width is decre

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MathRevolution
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In a rectangle, the length is increased by 10%, and the width is decre [#permalink] In a rectangle, the length is increased by 10%, and the width is decre   Updated on: 13 Jun 2020, 11:01
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A
B
C
D
E

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15% (low)

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84% (01:15) correct 16% (01:45) wrong based on 45 sessions
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[GMAT math practice question]

In a rectangle, the length is increased by 10%, and the width is decreased by 10%. What percentage is the reduced area of the rectangle?

Attachment:
6.12 PS.png
6.12 PS.png [ 19.38 KiB | Viewed 1899 times ]


A. \(1{%}\)

B. \(5{%}\)

C. \(10{%}\)

D. \(15{%}\)

E. \(17{%}\)
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Official Answer
A

Originally posted by MathRevolution on 12 Jun 2020, 02:20.
Last edited by MathRevolution on 13 Jun 2020, 11:01, edited 2 times in total.
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yashikaaggarwal
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Re: In a rectangle, the length is increased by 10%, and the width is decre [#permalink] In a rectangle, the length is increased by 10%, and the width is decre   12 Jun 2020, 03:05
MathRevolution Sir I guess % sign is missing after 10, because there is no other case in which the change in area can be calculated. Kindly re-evaluate the question.
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Re: In a rectangle, the length is increased by 10%, and the width is decre [#permalink] In a rectangle, the length is increased by 10%, and the width is decre   12 Jun 2020, 03:17
It must be 10% increase and 10% decrease, then the OA is 1% decrease. Kindly edit
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Re: In a rectangle, the length is increased by 10%, and the width is decre [#permalink] In a rectangle, the length is increased by 10%, and the width is decre   12 Jun 2020, 04:07
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Let the length of original rectangle be L and breadth be B
Area = L*B -----------(1)

Length of changed rectangle = 1.1*L
Breadth of changed rectangle = 0.9*B
Area = 1.1*L*0.9*B = 0.99*L*B

Reduced area of rectangle = original area - changed area
=L*B - 0.99*L*B => 0.01*L*B

The percentage change = 0.01*L*B*100/1 => 1

Answer is A

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Re: In a rectangle, the length is increased by 10%, and the width is decre [#permalink] In a rectangle, the length is increased by 10%, and the width is decre   14 Jun 2020, 18:54
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=>

Assume \(a = AD\) and \(b = AB\) are the lengths of the two sides of rectangle \(ABCD\), as shown in the figure.

Then the area of the rectangle \(ABCD\) is \(ab.\)

Then the area of the rectangle \(AB’C’D’\) is \(a(1 - 0.1)·b(1 + 0.1) = ab(1 - 0.01)\) after the sides change.

Thus, the area is decreased by \(1%.\)

Therefore, A is the answer.
Answer: A
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Re: In a rectangle, the length is increased by 10%, and the width is decre [#permalink]
14 Jun 2020, 18:54
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