Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: Do the diagonals of a Quadrilateral ABCD bisect each other [#permalink]
30 Apr 2012, 01:19
1
This post received KUDOS
Expert's post
kotela wrote:
Do the diagonals of a quadrilateral ABCD bisect each other perpendicularly?
(1) AB=AD (2) BC=DC
It would be better if the question asked whether the diagonals cut each other perpendicularly, rather than bisect (not to confuse with perpendicular bisection).
For (1)+(2) we get that two pairs of adjacent sides are equal, so ABCD is a kite: a kite is a quadrilateral with two distinct pairs of equal adjacent sides.
Attachment:
Kite.png [ 9.96 KiB | Viewed 3427 times ]
Since diagonals of a kite intersect at right angles, then the answer to the question is YES, the diagonals cut each other perpendicularly. Sufficient.
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
03 May 2012, 20:42
When we combine (1)+(2), after fixing point A,B,D according to the first condition, C must lie on the perpendicular bisector of BD in order to satisfy BC=CD. Hence (C).
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
04 May 2012, 13:33
Bunuel wrote:
pinchharmonic wrote:
bunuel,
did the problem come with a diagram? i'm a bit confused on how you arrived at a kite. two adjacent sides being equal could be a square or a rhombus.
and I don't know the rule, but it appears that a square/rhombus do not have diagonals that cut at 90 degrees.
thanks for your help!
The diagonals of both square and rhombus cut at 90 degrees.
bunuel, thanks, with that said, can you elaborate on how you visualized the problem and ended at a kite? should the solution encompass that ABCD must be = kite/rhombus/squre and those all have 90 degree intersecting diagonals?
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
04 May 2012, 13:51
Expert's post
pinchharmonic wrote:
Bunuel wrote:
pinchharmonic wrote:
bunuel,
did the problem come with a diagram? i'm a bit confused on how you arrived at a kite. two adjacent sides being equal could be a square or a rhombus.
and I don't know the rule, but it appears that a square/rhombus do not have diagonals that cut at 90 degrees.
thanks for your help!
The diagonals of both square and rhombus cut at 90 degrees.
bunuel, thanks, with that said, can you elaborate on how you visualized the problem and ended at a kite? should the solution encompass that ABCD must be = kite/rhombus/squre and those all have 90 degree intersecting diagonals?
The question is whether the diagonals cut at 90 degrees, we know for sure that ABCD is a kite so we can answer YES to the question. ABCD can also be a rhombus or a square but that's not relevant anymore. _________________
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
04 May 2012, 14:13
thanks again bunuel! i see what you mean now. the two statements AT MOST tell you it is a kite. whereas we'd require more restrictions for it to be a rhombus, square, etc.
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
05 May 2012, 14:48
1
This post received KUDOS
Kinds of quadrilaterals: 1) Square 2) rectangle 3) Trapezoid 4) Rhombus and 5) Kite
well quadrilaterals whose adjacent sides are equal can be 1) Square 2) Rhombus and 3) Kite and all three diagonals cut each other at 90 degrees
so option one tells us that it is either a square or a rhombus or a kite , isn't this sufficient to answer yes to the question ..
similarly option b too tells us that this quadrilateral could be a 1) Square 2) Rhombus or a 3) Kite and all three diagonals cut each other at 90 degrees, so shouldn't be sufficient too
are there any quadrilaterals whose adjacent sides could be equal apart from these 3, whose Diagonals do not cut each other at 90.
In short can someone more elaborate on how either of the statements are insufficient
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
06 May 2012, 00:51
Expert's post
BhaskarPaul wrote:
Kinds of quadrilaterals: 1) Square 2) rectangle 3) Trapezoid 4) Rhombus and 5) Kite
well quadrilaterals whose adjacent sides are equal can be 1) Square 2) Rhombus and 3) Kite and all three diagonals cut each other at 90 degrees
so option one tells us that it is either a square or a rhombus or a kite , isn't this sufficient to answer yes to the question ..
similarly option b too tells us that this quadrilateral could be a 1) Square 2) Rhombus or a 3) Kite and all three diagonals cut each other at 90 degrees, so shouldn't be sufficient too
are there any quadrilaterals whose adjacent sides could be equal apart from these 3, whose Diagonals do not cut each other at 90.
In short can someone more elaborate on how either of the statements are insufficient
thanks
Sometimes it's better to draw an actual diagram to test theoretical reasoning. The fact that two sides of a quadrilateral are equal DOES NOT mean that its' either a kite, a square, or a rhombus:
Attachment:
Sides.png [ 2.1 KiB | Viewed 3151 times ]
You can consider two equal sides to be either AB and AD or BC and DC and see that neither of statement is sufficient on its own.
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
06 May 2012, 15:40
1
This post received KUDOS
Bunuel wrote:
BhaskarPaul wrote:
Kinds of quadrilaterals: 1) Square 2) rectangle 3) Trapezoid 4) Rhombus and 5) Kite
well quadrilaterals whose adjacent sides are equal can be 1) Square 2) Rhombus and 3) Kite and all three diagonals cut each other at 90 degrees
so option one tells us that it is either a square or a rhombus or a kite , isn't this sufficient to answer yes to the question ..
similarly option b too tells us that this quadrilateral could be a 1) Square 2) Rhombus or a 3) Kite and all three diagonals cut each other at 90 degrees, so shouldn't be sufficient too
are there any quadrilaterals whose adjacent sides could be equal apart from these 3, whose Diagonals do not cut each other at 90.
In short can someone more elaborate on how either of the statements are insufficient
thanks
Sometimes it's better to draw an actual diagram to test theoretical reasoning. [color=#FF4040]The fact that two sides of a quadrilateral are equal DOES NOT mean that its' either a kite, a square, or a rhombus:[/color]
Attachment:
Sides.png
You can consider two equal sides to be either AB and AD or BC and DC and see that neither of statement is sufficient on its own.
Hope it's clear.
Hi
I meant two Adjacent sides not any two sides . If two adjacent sides are equal then it must be either a square or a rhombus or a kite , must it not ?
Can you paste a figure of a quadrilateral , with two ADJACENT sides equal , but it must not be a square , a rhombus or a kite , this would certainly make either statements insufficient individually , as any other figure apart from these 3 , will not cut at 90 degrees ,
Re: Do the diagonals of a quadrilateral ABCD bisect each other [#permalink]
06 May 2012, 22:27
Expert's post
Joy111 wrote:
Bunuel wrote:
BhaskarPaul wrote:
Kinds of quadrilaterals: 1) Square 2) rectangle 3) Trapezoid 4) Rhombus and 5) Kite
well quadrilaterals whose adjacent sides are equal can be 1) Square 2) Rhombus and 3) Kite and all three diagonals cut each other at 90 degrees
so option one tells us that it is either a square or a rhombus or a kite , isn't this sufficient to answer yes to the question ..
similarly option b too tells us that this quadrilateral could be a 1) Square 2) Rhombus or a 3) Kite and all three diagonals cut each other at 90 degrees, so shouldn't be sufficient too
are there any quadrilaterals whose adjacent sides could be equal apart from these 3, whose Diagonals do not cut each other at 90.
In short can someone more elaborate on how either of the statements are insufficient
thanks
Sometimes it's better to draw an actual diagram to test theoretical reasoning. [color=#FF4040]The fact that two sides of a quadrilateral are equal DOES NOT mean that its' either a kite, a square, or a rhombus:[/color]
Attachment:
Sides.png
You can consider two equal sides to be either AB and AD or BC and DC and see that neither of statement is sufficient on its own.
Hope it's clear.
Hi
I meant two Adjacent sides not any two sides . If two adjacent sides are equal then it must be either a square or a rhombus or a kite , must it not ?
Can you paste a figure of a quadrilateral , with two ADJACENT sides equal , but it must not be a square , a rhombus or a kite , this would certainly make either statements insufficient individually , as any other figure apart from these 3 , will not cut at 90 degrees ,
Thanks
Adjacent sides are sides having have a common vertex. In the diagram in my previous post two adjacent sides are equal (the sides crossed with little line segments). _________________
Re: Do the diagonals of a Quadrilateral ABCD bisect each other [#permalink]
30 Apr 2014, 08:19
Bunuel wrote:
kotela wrote:
Do the diagonals of a quadrilateral ABCD bisect each other perpendicularly?
(1) AB=AD (2) BC=DC
It would be better if the question asked whether the diagonals cut each other perpendicularly, rather than bisect (not to confuse with perpendicular bisection).
For (1)+(2) we get that two pairs of adjacent sides are equal, so ABCD is a kite: a kite is a quadrilateral with two distinct pairs of equal adjacent sides.
Attachment:
Kite.png
Since diagonals of a kite intersect at right angles, then the answer to the question is YES, the diagonals cut each other perpendicularly. Sufficient.
Answer: C.
Yes, It would be better if Bisection was completely removed from this question as we are only testing for perpendicularity. if the question is asking for both perpendicular and bisection of the Diagonals using 1+2 we can have the following figures a kite - no ( here only one Diagonal is Bisected not both ) square - yes rhombus- no
answer E
If Bisect is removed and only we are checking for diagonals perpendicularity then using 1+ 2 we can have the following figures -> square - yes -> rhombus - yes --> kite -- yes
Answer C
Members please share your views.Thank you.
gmatclubot
Re: Do the diagonals of a Quadrilateral ABCD bisect each other
[#permalink]
30 Apr 2014, 08:19
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...