Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 16 Feb 2011
Posts: 195
Schools: ABCD

If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
23 May 2011, 08:41
10
This post was BOOKMARKED
Question Stats:
46% (01:25) correct 54% (01:03) wrong based on 74 sessions
HideShow timer Statistics
If A, B, C and D form a quadrilateral. Is AC > BD ? (1) Angle ABC < Angle BCD (2) AB = BC= CD = DA
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 11 Jul 2013, 00:58, edited 1 time in total.
Edited the question.



Intern
Joined: 31 Mar 2011
Posts: 1

Re: GMATClub <700+> question [#permalink]
Show Tags
23 May 2011, 11:14
I thought it this way. Take two points on a line segment, let it be B and C. Now draw two infinite lines from points B and C such that angle B < angle C (condition a). Fix one point on any one of the line segments, say it A. Now you can vary point D on other line segment giving different length of diagonals. So insufficient. Hope it helps



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1260

Re: GMATClub <700+> question [#permalink]
Show Tags
24 May 2011, 00:01
a+b imagine a kite. In that the diagonals AC= BD means all the angles are equal too. However, angle ABC<BCD means even if all sides are equal, diagonal BD> AC. drawing this will help to understand it surely. C
_________________
Visit  http://www.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



Manager
Joined: 07 Jun 2011
Posts: 66

Re: GMATClub <700+> question [#permalink]
Show Tags
15 Aug 2011, 00:04
I first thought both diagonals of a rhombus are equal but apparently the diagonal opposite to the wider angle is more in length than the other diagonal...
there for C
based on statement 2 we can conclude the two possibilities as Square and rhombus
so not sufficient
stament 1 is obviously not sufficient. Combining both the information we can conclude the figure as rhombus and with the angle gives we can determine which diagonal is more in length



Manager
Joined: 04 Jun 2011
Posts: 182

Re: GMATClub <700+> question [#permalink]
Show Tags
15 Aug 2011, 01:11
nice question!! for a min i forgot rhombus...



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
15 Nov 2013, 09:23
voodoochild wrote: If A, B, C and D form a quadrilateral. Is AC > BD ?
(1) Angle ABC < Angle BCD (2) AB = BC= CD = DA Is there a nice OE for this one? From my understanding the question is asking whether the diagonals are equal right? But, I'm afraid I didn't get the right answer. Will an expert please elaborate on this one? Happy to provide some Kudos if needed Cheers! J



Senior Manager
Joined: 13 May 2013
Posts: 456

Re: If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
10 Dec 2013, 15:04
4
This post received KUDOS
If A, B, C and D form a quadrilateral. Is AC > BD ?
(1) Angle ABC < Angle BCD
This tells us that ABCD is not a square or a rectangle because naturally, both have four angles each equaling 90 degrees. With a triangle, the leg across from the largest angle is the longest but does it work like that with a four sided figure? Apparently not because 1 is not sufficient.
(2) AB = BC= CD = DA
This tells us that ABCD is either a square or a rhombus. If the figure is a square, then both diagonals AC = BD. If the figure is a rhombus, then one diagonal will be longer than the other. Insufficient.
1+2) This tells us that all four sides are equal and that one angle (or in this case, pairs of angles) is greater than another. The only possible shape that has four equal sides and different interior angles is a Rhombus. AC > BD. Sufficient.



Current Student
Joined: 06 Sep 2013
Posts: 1954
Concentration: Finance

Re: If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
10 Dec 2013, 15:23
WholeLottaLove wrote: If A, B, C and D form a quadrilateral. Is AC > BD ?
(1) Angle ABC < Angle BCD
This tells us that ABCD is not a square or a rectangle because naturally, both have four angles each equaling 90 degrees. With a triangle, the leg across from the largest angle is the longest but does it work like that with a four sided figure? Apparently not because 1 is not sufficient.
(2) AB = BC= CD = DA
This tells us that ABCD is either a square or a rhombus. If the figure is a square, then both diagonals AC = BD. If the figure is a rhombus, then one diagonal will be longer than the other. Insufficient.
1+2) This tells us that all four sides are equal and that one angle (or in this case, pairs of angles) is greater than another. The only possible shape that has four equal sides and different interior angles is a Rhombus. AC > BD. Sufficient. WholeLotta Love for you buddy! +1 Kudos Cheers! J



Manager
Joined: 17 Mar 2014
Posts: 70

Re: If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
14 May 2014, 04:00
voodoochild wrote: If A, B, C and D form a quadrilateral. Is AC > BD ?
(1) Angle ABC < Angle BCD (2) AB = BC= CD = DA To show more clearly why 1 is not sufficient , here are 2 figures. Both have angle B less than angle C Hence 1 is insufficient. Attachment:
Kite.jpg [ 119.23 KiB  Viewed 1923 times ]



NonHuman User
Joined: 09 Sep 2013
Posts: 13801

Re: If A, B, C and D form a quadrilateral. Is AC > BD ? [#permalink]
Show Tags
07 Sep 2015, 23:24
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 22 Apr 2015
Posts: 1

If points A , B , C , and D form a quadrilateral [#permalink]
Show Tags
23 Jan 2016, 23:19
If points A , B , C , and D form a quadrilateral, is AC longer than BD ?
1. ∠ABC>∠BCD 2. AB=BC=CD=DA
Can you please help me out why the triangle property of the sides opposite to the greater angle has the greater length not applicable in statement A?



Math Expert
Joined: 02 Aug 2009
Posts: 5660

Re: If points A , B , C , and D form a quadrilateral [#permalink]
Show Tags
23 Jan 2016, 23:56
ranajoy42 wrote: If points A , B , C , and D form a quadrilateral, is AC longer than BD ?
1. ∠ABC>∠BCD 2. AB=BC=CD=DA
Can you please help me out why the triangle property of the sides opposite to the greater angle has the greater length not applicable in statement A? Hi, I am merging your topic as the same has been discussed.. you can go through the solution.. Specific to your Q.. the angles are of two different triangles ABC and BCD, but the property of the sides opposite to the greater angle has the greater length is applicable in the same triangle..Hope it helps
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
BANGALORE/



Manager
Joined: 04 Jul 2017
Posts: 61
Location: India
Concentration: Marketing, General Management
Schools: HBS '20, Stanford '20, Wharton '20, Sloan '20, CBS '20, Tuck '20, Yale '20, Johnson '20, INSEAD Jan '19, Insead Sept'18, ISB '19
GPA: 1
WE: Analyst (Consulting)

If points A, B, C and D form a quardrilateral, is AC longer than BC? [#permalink]
Show Tags
26 Aug 2017, 07:15
DS: If points A, B, C and D form a quardrilateral, is AC longer than BC? Stmt 1: Angle ABC > Angle BCD. Stmt 2: AB=BC=CD=DA. Guys this question is already answered here: https://gmatclub.com/forum/m14q32quad ... 76743.html But, I have a different question. When I started solving and drew a quadrilateral, I got confused what if the quadrilateral is drawn like ACBD? Coz this is a DS question and one needs to consider all the possibilities and in ACBD you can't have AC and BC as diagonals but they will be sides. Am I just thinking too far, and if yes, how should I limit myself from thinking this far? Thanks in advance.




If points A, B, C and D form a quardrilateral, is AC longer than BC?
[#permalink]
26 Aug 2017, 07:15






