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# The length and width of a painted rectangle were each increa

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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The length and width of a painted rectangle were each increa [#permalink]  10 Jun 2018, 05:15
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Question Stats:

92% (00:40) correct 7% (00:35) wrong based on 65 sessions
The length and width of a painted rectangle were each increased by 10%.

 Quantity A Quantity B The percent increase in the area of the painted rectangle 10%

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2917 [0], given: 394

Re: The length and width of a painted rectangle were each increa [#permalink]  14 Jul 2018, 04:39
Expert's post
Explanation

Choose smart numbers for the dimensions of the rectangle—for instance, length = 20 and width = 10.

The original area of the rectangle = length × width = 200. After a 10% increase for both the length and the width, the area becomes 22 × 11 = 242.

Use the formula for percent change:

Percent Change =$$\frac{Difference}{Original} \times 100\%$$=$$\frac{242-200}{200} \times 100\%=21\%$$

Quantity A is greater.

Alternatively, use logic. The formula for area requires multiplying the length and the width. If just one side is increased by 10%, then the overall area will increase by 10%. If two sides are increased by 10%, then the overall area will increase by more than 10%.
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Re: The length and width of a painted rectangle were each increa [#permalink]  01 May 2020, 04:30
Smart numbers to the rescue!

A square is a rectangle so I chose the same length and width.

Original length = 10
Original width = 10
Original area = 10*10 = 100

New length = 10+10% = 11
New width = 10+10% = 11
New area = 11*11 = 121

Using percent change formula: (new - old) / old --> (121-100) / 100 = 21/100 = 21%

21% is greater than 10%, therefore answer is A.
Re: The length and width of a painted rectangle were each increa   [#permalink] 01 May 2020, 04:30
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