Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Dec 2013, 11:11

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is quadrilateral ABCD a rectangle? Rephrase: does ABCD have

Author Message
TAGS:
Manager
Joined: 24 Jul 2009
Posts: 195
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4

Kudos [?]: 21 [0], given: 10

Is quadrilateral ABCD a rectangle? Rephrase: does ABCD have [#permalink]  23 Jan 2010, 20:18
00:00

Difficulty:

5% (low)

Question Stats:

46% (01:19) correct 53% (00:39) wrong based on 15 sessions
[Reveal] Spoiler:
Rephrase: does ABCD have 1)opposite sides that are parallel and equal, 2) bisecting diagonals and 3) opposite and equal angles of 90; adjacent angles that sum to 180.

(1) Line segments AC and BD bisect one another.
[Reveal] Spoiler:
Bisecting diagonals make quadrilateral ABCD a parallelogram but not necessarily a rectangle.

(2) Angle ABC is a right angle.
[Reveal] Spoiler:
One right angle isn't enough to establish that quadrilateral ABCD is a rectangle.

[Reveal] Spoiler:
Answer C: A paralleogram with one right angle has all right angles because opposite angles are equal. Therefore ABCD is a rectangle.

Source: MGMAT question bank

I posted this because of how it means you recall the properties of parallelograms.
_________________

Reward wisdom with kudos.

 Manhattan GMAT Discount Codes Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes
Manager
Joined: 27 Apr 2008
Posts: 192
Followers: 1

Kudos [?]: 24 [0], given: 1

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  24 Jan 2010, 17:41
Are there diagrams to these questions?
Manager
Joined: 10 Feb 2010
Posts: 197
Followers: 2

Kudos [?]: 25 [0], given: 6

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  17 Feb 2010, 20:19
gottabwise wrote:
[Reveal] Spoiler:
Rephrase: does ABCD have 1)opposite sides that are parallel and equal, 2) bisecting diagonals and 3) opposite and equal angles of 90; adjacent angles that sum to 180.

(1) Line segments AC and BD bisect one another.
[Reveal] Spoiler:
Bisecting diagonals make quadrilateral ABCD a parallelogram but not necessarily a rectangle.

(2) Angle ABC is a right angle.
[Reveal] Spoiler:
One right angle isn't enough to establish that quadrilateral ABCD is a rectangle.

[Reveal] Spoiler:
Answer C: A paralleogram with one right angle has all right angles because opposite angles are equal. Therefore ABCD is a rectangle.

Source: MGMAT question bank

I posted this because of how it means you recall the properties of parallelograms.

Senior Manager
Joined: 19 Nov 2007
Posts: 479
Followers: 3

Kudos [?]: 37 [0], given: 4

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  25 Feb 2010, 19:10
no diagrams????
_________________

-Underline your question. It takes only a few seconds!
-Search before you post.

Manager
Joined: 29 Oct 2009
Posts: 203
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Followers: 2

Kudos [?]: 48 [0], given: 12

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  26 Feb 2010, 07:30
Statement 1: Line segments AC and BD bisect one another. This is the case for rectangle, square and rhombus.
Not suff.
Stetement 2: Angle ABC is a right angle.
Any quadrilateral can have one right angle and other different angle. Not Suff.

Combining both statements could give us either rectangle or a square. Not suff.
Manager
Joined: 24 Jul 2009
Posts: 195
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4

Kudos [?]: 21 [0], given: 10

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  26 Feb 2010, 12:50
Sorry for the delay folks. Diagrams were not provided with the original question.
_________________

Reward wisdom with kudos.

Manager
Joined: 25 Jul 2010
Posts: 177
WE 1: 4 years Software Product Development
WE 2: 3 years ERP Consulting
Followers: 5

Kudos [?]: 19 [0], given: 15

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  07 Aug 2010, 14:31
Statement 1: Line segments AC and BD bisect one another. This is the case for rectangle, square and rhombus.
Not suff.
Stetement 2: Angle ABC is a right angle.
Any quadrilateral can have one right angle and other different angle. Not Suff.

Combining both statements could give us either rectangle or a square. Not suff.

But isn't square a specific case of rectangle. That way i would say answer is C
_________________

Intern
Joined: 21 Jan 2010
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  08 Aug 2010, 18:23
I agree with arundas, squares are technically rectangles. Rectangles aren't always squares
Intern
Joined: 30 Mar 2010
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 5

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  21 Aug 2010, 06:57
OK! What if it is a right trapezoid? I mean it will have one (even two) right angles, the segments AC and BD will bisect one another and at the same time it will not be a rectagle. What in this case?
Intern
Joined: 03 Aug 2010
Posts: 13
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 10:46
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

Senior Manager
Joined: 18 Jun 2010
Posts: 303
Schools: Chicago Booth Class of 2013
Followers: 19

Kudos [?]: 117 [0], given: 194

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 12:23
It's "С"

Last edited by Financier on 22 Aug 2010, 22:23, edited 1 time in total.
Intern
Joined: 30 Mar 2010
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 5

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 12:27
pankajattri wrote:
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

OK! This is a right trapezoid. Two angles are right and diagonals bisect one another. Still it is not a rectangle. I know the question is stupid... but I just want to find a flaw in my reasoning.
Attachments

trapezoid.jpg [ 10.88 KiB | Viewed 3366 times ]

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 695
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 14

Kudos [?]: 60 [0], given: 15

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 13:13
Financier
Ok I must admit I am confused. Diagonals of a trapezoid bisect each other?
a). Diagonals of quadrangle allways bisect each other.
b). Trapezoid is a specific case of quadrangle .
I don't think that the diagonals of a trapezoid bisect each other.

Financier wrote:
pankajattri wrote:
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

Dear Pankajattri,

First of all, I strongly suggest that you review the basics of Geometry so that you could recall that:
a). Diagonals of quadrangle allways bisect each other.
b). Trapezoid is a specific case of quadrangle .

Second, the Rules of GMATclub suppose that folks do not just utter statements without any foundation,
but rather unveil what rules they are based on. Above are the statements that prove that diagonals of Trapezoid intersect each other.

Third, the correct answer is E.

_________________

Consider kudos, they are good for health

Intern
Joined: 03 Aug 2010
Posts: 13
Followers: 0

Kudos [?]: 3 [1] , given: 0

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 17:04
1
KUDOS
Dear Financier,

Even If I was wrong, which by the way I am not, I don't know why couldn't you find a more suitable way of posting your comment.

As for as the question is concerned; the diagonals of a PARALLELOGRAM bisect each other and not of each QUADRANGLE. All parallelograms are quadrangles but not vice versa.

I really hope that you know what does "bisection", "quadrangle" and "parallelogram" mean.

And next time please do not utter statements without any foundation.
Senior Manager
Joined: 18 Jun 2010
Posts: 303
Schools: Chicago Booth Class of 2013
Followers: 19

Kudos [?]: 117 [0], given: 194

Re: DS Geometry: Is a ABCD a rectangle? [#permalink]  22 Aug 2010, 22:22
Pankajattri,

I was wrong, excuse me and my tone. I'm soooo sorry. I messed up words "bisect" and "intersect". This happens when people study a lot. The correct answer is "C".
Intern
Joined: 29 Aug 2012
Posts: 26
Schools: Babson '14
GMAT Date: 02-28-2013
Followers: 0

Kudos [?]: 1 [0], given: 56

Re: Is quadrilateral ABCD a rectangle? Rephrase: does ABCD have [#permalink]  14 Nov 2012, 12:10
Guys just wanted to add . as I had little confusion when I first saw this question --

From (1) ----> The diagonals bisect each other , ----> its a ||gm , for it to be a recrangle both diagonals should be equal.
From(2) ----> |_ ABC= 90 ----> clearly not sufficient.

When we combine both 1 & 2 ----> Its a ||gm with one angle 90. ----> that has to be a rectangle and both diagonals become automatically equivalent.
Re: Is quadrilateral ABCD a rectangle? Rephrase: does ABCD have   [#permalink] 14 Nov 2012, 12:10
Similar topics Replies Last post
Similar
Topics:
Is quadrilateral ABCD a rectangle? (A top left clockwise to 10 26 Oct 2005, 06:41
Is quadrilateral ABCD a rectangle? (1) Line segments AC and 4 28 Aug 2007, 20:19
Is quadrilateral ABCD a rectangle? (1) Angle ABC and BCD are 10 06 Sep 2007, 19:26
Is quadrilateral ABCD a rectangle? 6 09 Sep 2010, 06:42
1 Is quadrilateral ABCD a rectangle? 1 16 Jul 2013, 18:23
Display posts from previous: Sort by