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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri May 25, 2012 3:23 am
GmatKiss wrote:Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD
By definition rhombus is a quadrilateral whose all four sides are of equal length.

Statement 1: As the diagonals of ABCD are perpendicular bisectors of each other all the four sides of the quadrilateral are of equal length.
Sufficient

Statement 2: All the four sides of ABCD are of equal length.

Sufficient

The correct answer is D.
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by [email protected] » Fri May 25, 2012 3:45 am
According to me the correct answer is E.

Statement 1: says that the diagonals are perpendicular bisectors. But even other quadrilaterals like Kite and square have diagonals that are perpendicular bisectors. Hence statement 1 alone is insufficient.

Statement 2: says that all the sides are equal. But that is true for square as well. Hence statement 2 alone is also insufficient.

Combined: Kite gets canceled out and two such quadrilaterals exist. They are square and rhombus.

Hence even both statements combined do not give the answer. Hence the correct answer is E.

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by Anurag@Gurome » Fri May 25, 2012 3:56 am
[email protected] wrote:...But even other quadrilaterals like Kite and square have diagonals that are perpendicular bisectors
Kites do have diagonals that are perpendicular to each other but not they are not bisectors of each other.
[email protected] wrote:But that is true for square as well
All squares are by definition rhombuses.
Square is a special type of rhombus whose all the four angles are right angles.
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by patanjali.purpose » Fri May 25, 2012 4:06 am
[email protected] wrote:According to me the correct answer is E.

Statement 1: says that the diagonals are perpendicular bisectors. But even other quadrilaterals like Kite and square have diagonals that are perpendicular bisectors. Hence statement 1 alone is insufficient.

Statement 2: says that all the sides are equal. But that is true for square as well. Hence statement 2 alone is also insufficient.

Combined: Kite gets canceled out and two such quadrilaterals exist. They are square and rhombus.

Hence even both statements combined do not give the answer. Hence the correct answer is E.

Hope this is the correct answer ....
SQAURE is a ROMBUS and therefore IMO C

Moreover taking Anurag's point, IMO S2 is not sufficient as sides are same for RECTANGLE ALSO but rectangle is not rombus
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by [email protected] » Fri May 25, 2012 10:02 am
Patanjali! all sides of a Rectangle are not equal... And statement 2 of our question, says that
AB = BC = CD = AD.

This is what it is...

But a square is a rhombus was a new point for me so got stuck...
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by [email protected] » Fri May 25, 2012 10:35 am
Yes agreed, anurag is right... Kite does not have diagonals as perpendicular bisectors of each other. It has the longer diagonal as the perpendicular bisector of the shorter one. But the shorter one is not a perpendicular bisector of the longer one...

I did not get the difference initially... Thank You very much...

I hope everyone got the difference very easily...
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by patanjali.purpose » Fri May 25, 2012 12:01 pm
[email protected] wrote:Patanjali! all sides of a Rectangle are not equal... And statement 2 of our question, says that
AB = BC = CD = AD.

This is what it is...

But a square is a rhombus was a new point for me so got stuck...
Thanks. I agree. Anurag is CORRECT - I was wrong.

Thanks. Answer should be D
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