Is Quadrilateral ABCD a Square? 1) Diagonals of ABCD Bisect each oth

Question

Is Quadrilateral ABCD a Square?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source:  https://www.GMATInsight.com

Bunuel · Accepted Answer

mcmoorthy · Answer

Imho C

Statement 1: diagonals of both square and rhombus bisect at 90 degrees. Can't say certainly as square. Hence not sufficient.
Statement 2: diagonals of both rectangle and square are equal. Can't say certainly as square. Hence not sufficient.

Combining 1 and 2 the quadrilateral with equal diagonals bisecting each other at 90 degrees is a square hence sufficient.

Ans C

Sent from my iPad using GMAT Club Forum

aggvipul · Answer

for a square- diagonals should cut at 90 degrees and should be equal, answer C

SiffyB · Answer

STATEMENT 1: The diagonals of both a square and a kite (or rhombus) intersect each other at 90 degrees. Thus, we can't be sure whether ABCD is a square. Insufficient. (BCE)

STATEMENT 2: The diagonals of both a square and a rectangle are equal in dimension. So, we can't be sure whther ABCD is a square.
Insufficient (CE)

Combining both statements gives us a unique answer. Clealy, only a square satisfies both conditions and, thus, ABCD is a square.

Answer: (C)

Rajashree123 · Answer

Is quadrilateral ABCD a square?
(1) ABCD is a rectangle. (2) AB = BC

can someone please help ?

1. not sufficient as no where mentioned sides are equal.
2. not sure about other two sides.

combining both we can deduct a rectangle with 4 sides equal = square.
as AB=BC hence cd=ad. c should be the ans. am I correct?

andreagonzalez2k · Answer

Answer is C but your reasoning in 1 is not correct. Rhombus also has equal sides. So having diagonals bisecting each other at 90 degrees and equal sides IS NOT sufficient to say that it is a square. So the correct reasoning is:
1- It can be a square or a rhombus.
2- It can be a square or a rectangle.
Combing them we have a square.

apurv09 · Answer

Hi  Bunuel ,

how do we know that this given quadrilateral is a parallelogram? isn't that a necessary condition for it to be a square.?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is Quadrilateral ABCD a Square? 1) Diagonals of ABCD Bisect each oth

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is Quadrilateral ABCD a Square? 1) Diagonals of ABCD Bisect each oth

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards