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Is quadrilateral ABCD a square?

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Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 04:05
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Difficulty:

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Question Stats:

43% (00:52) correct 57% (01:05) wrong based on 99 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.

I am always struggling with such questions. Any sources to prepare for those?
[Reveal] Spoiler: OA

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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 05:41
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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New post 28 Sep 2015, 05:52
Answer is D, the second cannot be a kite
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Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 06:04
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Expert's post
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
Symmetries_of_square.svg.png [ 30.7 KiB | Viewed 1031 times ]


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Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html


Last edited by Engr2012 on 28 Sep 2015, 11:32, edited 1 time in total.
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 06:07
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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Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 10:59
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
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

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Kudos [?]: 1719 [0], given: 302

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Math Forum Moderator
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Kudos [?]: 1690 [1], given: 792

Concentration: Finance, Strategy
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GPA: 3.7
WE: Engineering (Aerospace and Defense)
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Re: Is quadrilateral ABCD a square? [#permalink]

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New post 28 Sep 2015, 11:07
1
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KUDOS
Expert's post
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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: Is quadrilateral ABCD a square? [#permalink]

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Re: Is quadrilateral ABCD a square?   [#permalink] 16 Aug 2017, 04:47
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