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705-805 (Hard)|   Geometry|      
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vscid
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Quadrilateral ABCD is a rhombus and points C, D, and E are Updated on: 13 Oct 2013, 16:03
Originally posted by vscid on 09 Mar 2010, 20:10.
Last edited by Bunuel on 13 Oct 2013, 16:03, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

48% (02:25) correct 52% (02:26) wrong based on 163 sessions

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Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

OPEN DISCUSSION OF THIS QUESTION IS HERE: quadrilateral-abcd-is-a-rhombus-and-points-c-d-and-e-are-82126.html
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C
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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Quadrilateral ABCD is a rhombus and points C, D, and E are 09 Mar 2010, 20:36
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C should be the answer.

Join BD with a broken line to indicate an imaginary figure ABDE. AD as diagonal, we need both the given statements to prove that t'gle ABD and t'gle ADE are both congruent. Hence, Angles B and E are equal and opposite, so are angles A and D, and sides AB = BD = DE = AE.

Hence, ABDE will be a rhombus, if the given stimulus and statements are true.
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Quadrilateral ABCD is a rhombus and points C, D, and E are 13 Oct 2013, 15:59
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What's the OA for this one please? Is there anyone else that might want to give it a shot?
I got (C) but really more because of intuition than because I can explain it clearly.

Experts please advice on this very nice piece of question
Many thanks
Will provide some Kudos to good answers
Cheers
J:)
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Quadrilateral ABCD is a rhombus and points C, D, and E are 13 Oct 2013, 16:05
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jlgdr
vscid
Please see attached.

What's the OA for this one please? Is there anyone else that might want to give it a shot?
I got (C) but really more because of intuition than because I can explain it clearly.

Experts please advice on this very nice piece of question
Many thanks
Will provide some Kudos to good answers
Cheers
J:)
Show more


Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: quadrilateral-abcd-is-a-rhombus-and-points-c-d-and-e-are-82126.html
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