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

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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.?

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

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