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# Is quadrilateral ABCD a square?

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Retired Moderator
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28 Sep 2015, 03:05
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65% (hard)

Question Stats:

43% (01:11) correct 57% (01:16) wrong based on 291 sessions

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Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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28 Sep 2015, 04:41
Answer should be A

I also had the same issue. I went through all the properties of different quadrilaterals.

1. ABCD is a rectangle and if diagnals intersect at 90 degree, square is the only option. Suff.

2. In the second case, it can be either square or a kite as per the given properties Insuff.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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28 Sep 2015, 04:52
Answer is D, the second cannot be a kite
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Re: Is quadrilateral ABCD a square?  [#permalink]

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Updated on: 28 Sep 2015, 10:32
1
reto wrote:
Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

I am always struggling with such questions. Any sources to prepare for those?

reto, look at the attached picture of quadrilateral family in GMAT. It is taken from https://en.wikipedia.org/wiki/Rhombus

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.
Attachments

Symmetries_of_square.svg.png [ 30.7 KiB | Viewed 4164 times ]

Originally posted by ENGRTOMBA2018 on 28 Sep 2015, 05:04.
Last edited by ENGRTOMBA2018 on 28 Sep 2015, 10:32, edited 1 time in total.
Updated the picture
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Re: Is quadrilateral ABCD a square?  [#permalink]

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28 Sep 2015, 05:07
apoorva2890 wrote:
Answer should be A

I also had the same issue. I went through all the properties of different quadrilaterals.

1. ABCD is a rectangle and if diagnals intersect at 90 degree, square is the only option. Suff.

2. In the second case, it can be either square or a kite as per the given properties Insuff.

It can not be a kite as the resulting triangle must be RIGHT ANGLED ISOSCELES triangle. Kite does not provide that. Thus, square is the only option.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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28 Sep 2015, 09:59
Engr2012 wrote:
reto wrote:
Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

I am always struggling with such questions. Any sources to prepare for those?

reto, look at the attached picture of quadrilateral family in GMAT.

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.

Thanks - I also found this overview here: quadrilateral-properties-136155.html#p1106572
CEO
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Schools: Kellogg '18 (M)
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Re: Is quadrilateral ABCD a square?  [#permalink]

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28 Sep 2015, 10:07
1
reto wrote:
Engr2012 wrote:
reto wrote:
Is quadrilateral ABCD a square?

(1) ABCD is a rectangle whose diagonals intersect at right angles.
(2) AC, a diagonal of ABCD, is also the hypotenuse of isosceles right triangles ABC and ADC.

I am always struggling with such questions. Any sources to prepare for those?

reto, look at the attached picture of quadrilateral family in GMAT.

Statement 2, is sufficient to answer as it can only be a square. Kite would have been possible had the statement mentioned that the triangles are isosceles but not necessarily right angled.

Statement 1 eliminates rhombus as it is not a rectangle.

Thus D is the correct answer.

Thanks - I also found this overview here: quadrilateral-properties-136155.html#p1106572

Instead of just rote memorizing these properties make sure to draw them out so that you remember how to apply these properties as well.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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08 Jan 2018, 11:01
I don't understand why (1) is Suff.

Don't the diagonals of rhombus intersect at 90º?
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Re: Is quadrilateral ABCD a square?  [#permalink]

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08 Jan 2018, 19:50
Fernandocma wrote:
I don't understand why (1) is Suff.

Don't the diagonals of rhombus intersect at 90º?

(1) says that ABCD is a rectangle. Rectangular rhombus is a square.

Check Properties of Polygons Questions for similar problems.

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
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Hope it helps.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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Re: Is quadrilateral ABCD a square?   [#permalink] 15 Jan 2020, 06:02

# Is quadrilateral ABCD a square?

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