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# geometry

Author Message
Senior Manager
Joined: 17 Oct 2016
Posts: 321
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

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13 Oct 2017, 03:56
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:21) correct 0% (00:00) wrong based on 10 sessions

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What is the area of the shaded quadrilateral in the figure above?

(1) a^2−b^2=40

(2) a^2+b^2=58

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Intern
Joined: 30 Nov 2016
Posts: 38
Location: India
Concentration: Finance, Strategy

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13 Oct 2017, 04:11
statement 1 does not lead to any solution as we need the length of one of the sides of the shaded region.

Statement 2 on the other hand directly gives us the square of length the side.
a^{2} +b^{2}= 58 since all sides are equal the given info is sufficient.
Senior Manager
Joined: 17 Oct 2016
Posts: 321
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

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13 Oct 2017, 04:35
animesh mohanty wrote:
statement 1 does not lead to any solution as we need the length of one of the sides of the shaded region.

Statement 2 on the other hand directly gives us the square of length the side.
a^{2} +b^{2}= 58 since all sides are equal the given info is sufficient.

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Manager
Joined: 14 Sep 2016
Posts: 135

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13 Oct 2017, 04:45
The given figure is a square since each side is a+b. Hence, area of a square is (a+b)^2

We get 4 triangles if we cut out the quadrilateral from the given square. Since, each triangle is a right angle and we know that the area of a right angle triangle is 1/2 * (Base)* (Height).
So area of 4 triangles in terms of a and b = 2ab

Hence area of the quadilateral = area of the square - area of 4 trianlges
a^2+b^2+2ab - 2ab

hence area is a^2 + b^2

1) a^2 - b^2 = 40, Insufficient

2) a^2 + b^2 = 58, Sufficient

Intern
Joined: 30 Nov 2016
Posts: 38
Location: India
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13 Oct 2017, 04:48
statement 2 tells us a^2+b^2 =58
by using pythagorean theorem we find out that the length any of the sides of the shaded region is $$\sqrt{58}$$
Math Expert
Joined: 02 Sep 2009
Posts: 50700

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13 Oct 2017, 05:28
Sasindran wrote:
What is the area of the shaded quadrilateral in the figure above?

(1) a^2−b^2=40

(2) a^2+b^2=58

TOPIC IS LOCKED AND ARCHIVED.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: geometry &nbs [#permalink] 13 Oct 2017, 05:28
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