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# A rectangle is formed by increasing two opposite sides of a

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GMAT Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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A rectangle is formed by increasing two opposite sides of a [#permalink]  08 Apr 2018, 10:10
Expert's post
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Question Stats:

80% (00:15) correct 20% (00:50) wrong based on 5 sessions
A rectangle is formed by increasing two opposite sides of a square of side length x by y units, and decreasing the two remaining sides of the square by y units. What is the area of the rectangle?

A. $$4x$$
B. $$4x - 2y$$
C. $$x^2 - 2y$$
D. $$x^2 + 2y$$
E. $$x^2 - y^2$$

Drill 2
Question: 9
Page: 508
[/quote]
[Reveal] Spoiler: OA

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Manager
Joined: 26 Jan 2018
Posts: 172
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Kudos [?]: 104 [0], given: 3

Re: A rectangle is formed by increasing two opposite sides of a [#permalink]  08 Apr 2018, 21:06
One side is increased by y units, so x+y is the length.
One side is reduced by y units, so x-y is the breadth.

(x+y)(x-y) = x^2-y^2

GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: A rectangle is formed by increasing two opposite sides of a [#permalink]  18 Apr 2018, 15:34
Expert's post
Explanation

The dimensions of the new rectangle will be x + y and x – y.

To find the area of the rectangle, multiply the length by the width: $$(x + y)(x - y) = x^2 - y^2$$. The answer is choice (E).

Or, you can just plug in values for x and y.
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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: A rectangle is formed by increasing two opposite sides of a [#permalink]  22 Apr 2018, 12:22
Expert's post
Explanation

The best approach here is to Plug In.

First, try s = 2 and t = 3: Quantity A is (2 + 3)2 = 52 = 25, and Quantity B is 22 + 32 = 4 + 9 = 13.

Quantity A is greater, so eliminate choices (B) and (C). Next, make s and t both 0: Now Quantity A is $$(0)^2 = 0$$, and Quantity B is $$0^2 + 0^2 = 0$$.

Now the two quantities are equal, so eliminate choice (A), and you’re left with choice (D).
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Re: A rectangle is formed by increasing two opposite sides of a   [#permalink] 22 Apr 2018, 12:22
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