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Are all sides of quadrilateral ABCD equal?

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Bunuel
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Are all sides of quadrilateral ABCD equal? [#permalink] New post   23 Apr 2021, 01:30
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Are all sides of quadrilateral ABCD equal?

(1) The diagonals of ABCD bisect each other at right angles.

(2) ABCD is a parallelogram with three equal sides.


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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   23 Apr 2021, 03:20
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Are all sides of quadrilateral ABCD equal?

Statement (1) The diagonals of ABCD bisect each other at right angles.
Figure is a rhombus i.e all four sides are equal
Hence, sufficient

statement (2) ABCD is a parallelogram with three equal sides.
If three sides are equal of a parallelogram, fourth side got be of the same length as other three.

Hence, Sufficient

D is the answer IMO
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Are all sides of quadrilateral ABCD equal? [#permalink] New post   Updated on: 24 Apr 2021, 02:33
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I misread the stat 1. Corrected!

Are all sides of quadrilateral ABCD equal?

Stat1: The diagonals of ABCD bisect each other at right angles.
It can be a rhombus or Square. So, all sides are equal. Not sufficient.
Note- In kite, diagonals makes right angle, but doesn't bisect each other.

Stat2: ABCD is a parallelogram with three equal sides.
In parallelogram, opposite sides are equal and parallel. If 3 sides are equal then 4th sides will be equal too. Sufficient.

So, I think B. :)

Originally posted by TarunKumar1234 on 23 Apr 2021, 06:10.
Last edited by TarunKumar1234 on 24 Apr 2021, 02:33, edited 1 time in total.
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   23 Apr 2021, 09:10
Are all sides of quadrilateral ABCD equal?
Needs to be a definite yes/no.

(1) The diagonals of ABCD bisect each other at right angles.
Not sufficient. Could be either kite, rhombus or square.

(2) ABCD is a parallelogram with three equal sides.
Sufficient.

IMO B

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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   23 Apr 2021, 23:45
IMO B

St. 1 The diagonals of ABCD bisect each other at right angles -> it doesn’t give any info about sides as four sides might be equal and might not be. (Insufficient)
St. 2 ABCD is a parallelogram with three equal sides -> a parallelogram with three equal sides has to have the 4th side equal with its opposite side otherwise, figure will not be a parallelogram (Sufficient)
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   24 Apr 2021, 00:54
Are all sides of quadrilateral ABCD equal?

(1) The diagonals of ABCD bisect each other at right angles.
ABCD can be a square or a kite.
Not sufficient

(2) ABCD is a parallelogram with three equal sides.
In parallelogram, the opposite sides are parallel and equal. If three sides are equal, the fourth side has to be equal.
Sufficient

Option B

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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   25 Apr 2021, 20:55
Statement 1 could mean the figure is a rectangle too, right? If so, how is the statement sufficient?
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   25 Apr 2021, 21:23
Hi Bunuel
Please explain why D is the correct answer? I don't understand why statement 1 is sufficient?
Could anyone help explain?

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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   25 Apr 2021, 23:21
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imo D

Are all sides of quadrilateral ABCD equal?

Stat1: The diagonals of ABCD bisect each other at right angles.

It can be a rhombus or Square.
So, all sides are equal. sufficient.

Stat2: ABCD is a parallelogram with three equal sides.
In parallelogram, opposite sides are equal and parallel. If 3 sides are equal then 4th sides will be equal . Sufficient.
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Are all sides of quadrilateral ABCD equal? [#permalink] New post   16 May 2021, 09:23
chetan2u Bunuel

please explain the variation as below of posted question.In this stmt 2 is different from posted question

Are all sides of quadrilateral ABCD equal?
(1) The diagonals of ABCD bisect each other at right angles.
(2) ABCD is a parallelogram with two equal sides.
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   22 Oct 2021, 07:57
Bunuel wrote:
Are all sides of quadrilateral ABCD equal?

(1) The diagonals of ABCD bisect each other at right angles.

(2) ABCD is a parallelogram with three equal sides.


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Bunuel BrentGMATPrepNow

I believe this question never got its due. The OA seems to controversial. Please share the OE so that the confusion can be eliminated.
IMHO the answer should be Option B while the OA suggests D.
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   03 Nov 2021, 07:25
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Bunuel wrote:
Are all sides of quadrilateral ABCD equal?

(1) The diagonals of ABCD bisect each other at right angles.

(2) ABCD is a parallelogram with three equal sides.


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This question is a part of Are You Up For the Challenge: 700 Level Questions collection.
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Re: Are all sides of quadrilateral ABCD equal? [#permalink] New post   06 Nov 2021, 05:51
I believe this question's OA is not correct. There was a similar question where Bunuel himself proposed that kite allows for its' diagonals to be perpendicular to one another, thus making such a condition insufficient to call a figure rhombus. Also important to mention, that any square is a rhombus, since it's a parallelogram with 4 equal sides, so it's not an issue here.
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Re: Are all sides of quadrilateral ABCD equal? [#permalink]
06 Nov 2021, 05:51
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