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Mgmat quant prob set mistake?????- geometry quad qs

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astharpurohit
 Post subject: Mgmat quant prob set mistake?????- geometry quad qs
 Post Posted: Fri Nov 19, 2010 8:07 am 
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Students


Posts: 10
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

It says the ans is d
but it should be E- cause you can't eliminate that the quad could be a square, you need more info?
Or i m over analyzing it?
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atul.prasad
 Post subject: Re: Mgmat quant prob set mistake?????- geometry quad qs
 Post Posted: Fri Nov 19, 2010 4:20 pm 
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Students


Posts: 34
I guess the answer should be C..

1) It may not be a rhombus for the following:
http://postimage.org/image/3odchhok/

2) All rhombus are parallelograms. This statement does not confirm that

Together:
http://postimage.org/image/3z116090/

Its given that AB = AD and Angle AOD=AOB is 90 degree

We can prove that all 4 triangles are congruent to each other.

-Opposite angles of a rhombus have equal measure.
-The two diagonals of a rhombus are perpendicular.

From above we can conclude that it is a rhombus
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tim
 Post subject: Re: Mgmat quant prob set mistake?????- geometry quad qs
 Post Posted: Thu Nov 25, 2010 8:42 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
Atul, both of your diagrams are incorrect representations of the information given in the statements. The answer of course is D, and you need little more than the definitions of "rhombus" and "perpendicular bisector". 2 is trivially sufficient, because the definition of a rhombus is that all 4 sides are the same length. With statement 1, the diagonals split the figure into four triangles, all of which are right triangles (definition of "perpendicular") and all of which have congruent legs (definition of "bisector"). Thus all four triangles are congruent and so in particular their hypotenuses are all the same, again fulfilling the definition of "rhombus". The issue of whether this is a square is irrelevant, as all squares are automatically rhombuses as well..

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Tim Sanders
Manhattan GMAT Instructor
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