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ABCD Rhombus

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pahwa.suneet
 Post subject: ABCD Rhombus
 Post Posted: Fri Mar 25, 2011 9:57 am 
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Students


Posts: 1
Hi Guys,
I have a problem in below question from MGMAT Geometry question bank:
Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD


My problem is that statement (2) can also mean it is a square. But, the answer soln. states that each statement alone is sufficient.

Sincerely,
SP
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david.khoy
 Post subject: Re: ABCD Rhombus
 Post Posted: Mon Mar 28, 2011 3:46 am 
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Students


Posts: 30
A square is a rhombus with a right angle.

Statement 2 is sufficient, because a rhombus is a quadrilateral whose four sides all have the same length, regardless of the angles values.
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jnelson0612
 Post subject: Re: ABCD Rhombus
 Post Posted: Fri Apr 01, 2011 1:08 pm 
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ManhattanGMAT Staff


Posts: 1857
Thank you David.

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Jamie Nelson
ManhattanGMAT Instructor
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mengnu.liang
 Post subject: Re: ABCD Rhombus
 Post Posted: Sat Apr 14, 2012 12:26 pm 
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jnelson0612 wrote:
Thank you David.


Wait I thought ALL sides of Rhombus have to be equal. Statement 1 doesn't specify that. Shouldn't the answer be C?
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tim
 Post subject: Re: ABCD Rhombus
 Post Posted: Wed Apr 25, 2012 5:38 pm 
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ManhattanGMAT Staff


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Location: Southwest Airlines, seat 21C
statement 1 doesn't specify that, but if you draw any quadrilateral with diagonals that are perpendicular bisectors it will be a rhombus. remember in geometry problems you need to take what you are given and derive all implications from it. in this case, the implication is that we have a rhombus..

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Tim Sanders
Manhattan GMAT Instructor
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