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TAGS: Intern Joined: 07 Jan 2017
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Question Stats: 60% (00:18) correct 40% (00:31) wrong based on 5 sessions WXYZ is a parallelogram.

 Quantity A Quantity B Diagonal WY Diagonal XZ

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA
GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: WXYZ is a parallelogram [#permalink]
Expert's post
Explanation

Let a and b be the sides of the parallelogram and β be the angle in between a and b.

Formula of parallelogram diagonal in terms of sides and cosine β (cosine theorem). In this case β=100.

Diagonal XZ = $$\sqrt{a^2 + b^2 - 2ab cos(\beta)}$$ =$$\sqrt{a^2 + b^2 - 2ab cos(100)}$$ =$$\sqrt{a^2 + b^2 + 2ab cos(80)}$$.

Diagonal WY = $$\sqrt{a^2 + b^2 - 2ab cos(\beta)}$$ = $$\sqrt{a^2 + b^2 - 2ab cos(80)}$$.

Thus clearly XZ is greater. Hence option B is correct.

Alternatively you can just remember that in a parallogram the diagonal opposite to the larger angle is greater in length than the other one.
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Sandy
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Try our free Online GRE Test Re: WXYZ is a parallelogram   [#permalink] 14 Feb 2017, 15:38
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