Last visit was: 24 Jul 2024, 05:00 It is currently 24 Jul 2024, 05:00
Close
GMAT Club Daily Prep
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 17 Mar 2009
Posts: 133
Own Kudos [?]: 1919 [140]
Given Kudos: 21
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643489 [53]
Given Kudos: 86734
Send PM
User avatar
Intern
Intern
Joined: 14 Oct 2009
Posts: 45
Own Kudos [?]: 15 [8]
Given Kudos: 1
Location: India
Concentration: Consulting, General Management
Send PM
General Discussion
Retired Moderator
Joined: 05 Jul 2006
Posts: 847
Own Kudos [?]: 1575 [1]
Given Kudos: 49
Send PM
Re: Rhombus hard problem [#permalink]
1
Kudos
[quote="crejoc"]Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

to prove that it is a rhombus, we need to prove that it is a paralellogram with equal opposite angles and all sides =.

from 1

draw the diagonal bd would split the abcd rhombus into 2 similar triangles , both eqelateral all angles = 60, however as long as we dont know whether ae is // to bd or we know angles dae or aed we can not deduce that opposit sides of abde are equal or parallel.....insuff

from 2

obviously not suff

both

suff...C

Originally posted by yezz on 09 Aug 2009, 10:14.
Last edited by yezz on 15 Aug 2009, 12:05, edited 1 time in total.
Retired Moderator
Joined: 05 Jul 2006
Posts: 847
Own Kudos [?]: 1575 [0]
Given Kudos: 49
Send PM
Re: Rhombus hard problem [#permalink]
sandipchowdhury wrote:
whould you please explain why not B ?

to prove a shape to be a rhombus:
1)opposite sides are //
2) all sides are equal

and ( only to deferenciate it from a square):
3) opposite angles are =

to prove to be a square
same as above however all angles have to be = in measure and a such each = 90 degrees
User avatar
Manager
Manager
Joined: 13 Oct 2009
Affiliations: PMP
Posts: 153
Own Kudos [?]: 252 [1]
Given Kudos: 38
 Q48  V32
Send PM
Re: Rhombus hard problem [#permalink]
1
Bookmarks
I don't understand why not B.

question stem has given CDE is parallel to AB --> DE is parallel to AB

and S2 give AE is parallel to DB , so for ABDE, we have the condition that opposite sides are parallel is met.
How we know that opposite angles are not equal - can someone draw such figure ?
User avatar
Manager
Manager
Joined: 05 Oct 2008
Posts: 160
Own Kudos [?]: 3619 [0]
Given Kudos: 22
Send PM
Re: Rhombus [#permalink]
AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE)

Bunuel, all sides have to be equal as the question stem states that C, D and E are on the same line. And it also states that BD is parallel to AE. Try drawing any kind of rhombus with the following conditions and all sides will be equal. So why do we need statement A? Am I missing something?
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643489 [3]
Given Kudos: 86734
Send PM
Re: Rhombus [#permalink]
3
Kudos
Expert Reply
study wrote:
AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE)

Bunuel, all sides have to be equal as the question stem states that C, D and E are on the same line. And it also states that BD is parallel to AE. Try drawing any kind of rhombus with the following conditions and all sides will be equal. So why do we need statement A? Am I missing something?


From your reasoning above it's not clear how you came to the conclusion that alls sides must be equal.

Actually I don't even need to try drawing, to state that there are infinite # of cases possible for AE to be parallel to BD and ABDE not to be a rhombus. Just try to increase or decrease diagonal BD and leave everything else the same (AE||BD): you'll always have a parallelogram but in only one case a rhombus, when BD=AB.
User avatar
Intern
Intern
Joined: 26 Aug 2010
Posts: 44
Own Kudos [?]: 715 [7]
Given Kudos: 18
Location: India
Concentration: Finance
Send PM
Re: Rhombus hard problem [#permalink]
6
Kudos
1
Bookmarks
anandnat wrote:
I still don't understand why B is wrong. Can we safely say that the diagonal will never equal the side? If this is true, then with B, we always get a firm answer that ABDE is never a rhombus. Hence imo the answer is B. Math experts please help!


anandnat,

With statement 2, we can conclude that since AE is parallel to BD, therefore triangle ABD is mirror image of AED (similar triangle). We have, AD is equal to AB. With all this, we can assert that ED is equal to AB and AE is equal to BD.

In other way, to cut the long story short:-

From st 2, we can come closer to only this much.. :-D ..
ABD and AED are two similar "Isosceles" triangles, Joined together. But, we need to prove that all four sides are equal.

I have drawn one such example here:

Hope that helps!
Attachments

Rhombus1.jpg
Rhombus1.jpg [ 6.48 KiB | Viewed 70379 times ]

Rhombus1.jpg
Rhombus1.jpg [ 6.48 KiB | Viewed 70352 times ]


Originally posted by samark on 16 Oct 2010, 09:35.
Last edited by samark on 17 Oct 2010, 04:29, edited 1 time in total.
avatar
Intern
Intern
Joined: 03 Sep 2010
Posts: 7
Own Kudos [?]: 39 [2]
Given Kudos: 0
Send PM
Re: Rhombus hard problem [#permalink]
1
Kudos
1
Bookmarks
I will explain why B) is not sufficient

Pls refer the attached diagram

AE || BD is not sufficient to judge whether BD = DC or BD = BC because for AEDB to be a rhombus , AE = ED = DB= BA

From A) we can deduce

DC = CB = BD (diagonal of the rhombus) as angle B = angle C = angle D = 60 deg.

Now from the statement of the question , DC = AB as it is a rhombus , so DB = AB

Since from A) we deduce DB = AB and from 2) we know that AE = DB as C , D , E lies on a straight line

Hence combining (A) and (B) , we know that AEDB is always a RHOMBUS

Note that if angle BCD not equal to 60 degrees , then AEDB would not have been a RHOMBUS

Hope the above explanation is now clear
Attachments

rhombus-DS.doc [26 KiB]
Downloaded 287 times

avatar
Intern
Intern
Joined: 10 May 2012
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
I still don't understand this question. "AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. " I understand how paralellogram --> BD=AE and AB=DE, but how does AE||BD and BA||DA imply it is a paralellogram with opposite sides equal?
User avatar
Manager
Manager
Joined: 02 Sep 2012
Posts: 161
Own Kudos [?]: 579 [1]
Given Kudos: 99
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE:Architecture (Computer Hardware)
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
1
Kudos
Can some1 pls explain me how from st1 people derive BD=AB.Can anyone pls explain elaborately
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643489 [4]
Given Kudos: 86734
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
4
Kudos
Expert Reply
skamal7 wrote:
Can some1 pls explain me how from st1 people derive BD=AB.Can anyone pls explain elaborately


(1) The measure of angle BCD is 60 degrees. Since given that BC=DC, then <DBC=<BDC --> <DBC+<BDC+<BCD=180 degrees --> x+x+60=180 --> x=60 degrees. We have that triangle BCD is equilateral, thus BD=BC=DC. We know that AB=BC=CD=AD, thus BD=AB.

Hope it's clear.
User avatar
Manager
Manager
Joined: 28 Jul 2011
Posts: 224
Own Kudos [?]: 1402 [0]
Given Kudos: 16
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE:Accounting (Commercial Banking)
Send PM
Re: Rhombus [#permalink]
Bunuel wrote:
Attachment:
untitled.JPG
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


Bunnel,

In Statement 2 How can you say ABDE is ||gm without knowing whether AB and DE are ||el.... we just know that AE and BD are ||el
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643489 [1]
Given Kudos: 86734
Send PM
Re: Rhombus [#permalink]
1
Kudos
Expert Reply
mydreammba wrote:
Bunuel wrote:
Attachment:
untitled.JPG
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


Bunnel,

In Statement 2 How can you say ABDE is ||gm without knowing whether AB and DE are ||el.... we just know that AE and BD are ||el



We know that points C, D, and E are on the same line and since CD||AB, then the same line DE is also parallel to AB.

Hope it's clear.
User avatar
Senior Manager
Senior Manager
Joined: 13 Aug 2012
Posts: 328
Own Kudos [?]: 1844 [0]
Given Kudos: 11
Concentration: Marketing, Finance
GPA: 3.23
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
crejoc wrote:
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD


I think the rubber band technique is effective. If you can stretch a side or dimension and come up with different results, then the information is INSUFFICIENT.

1. If BCD is 60 then BAD is also 60. Then we are left with two angles from left to right with 120 each. Imagine a straight line cutting the rhombus in half horizontally, what we got are two equilateral triangles ABD and BCD. For ABDE to become a rhombus, AE, BD,DE, and AE must have equal sides. Imagine pulling the line CDE a little longer through pt. E, then we could distort the figure and come up with a non-rhombus quadrialeteral. We could push it back and we could estimate a rhombus.

INSUFFICIENT.

2. Now imagine your rhombus ABCD and make it narrower, this will make BD and AE's lengths shorter than the size of a side of rhombus ABCD. Imagine your rhombus a little wider and this will make BD and AE's lengths longer. By rubber band technique, we know that we are not sure if ABDE is a rhombus.

INSUFFICIENT.

Together:
We know that ABD and BCD are equilateral triangles forming rhombus ABCD. Thus, line BD would be equal to all the sides of the rhombus.
Now we know that BD and AE are parallel each other fixed by the bordering lines of BA and CDE. Hence, BD = AE.
All the sides of the rhombus are equal to BD then also to AE.

To close the deal, AB and DE must be equal to become a rhombus. Since AE and BD are two parallel lines with equal length then, we are certain that AB and DE are also equal in length.

Answer: C
avatar
Intern
Intern
Joined: 26 May 2013
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Hi Bunuel,

I think the answer to this Q shd be B. My soln is as follows:

let angle BAD be X, angle ABC be Y. Therefore since ABCD is a rhombus, angle BCD will be X and angle CDA will be Y. Also all the sides are equal of this rhombus, i.e., AB=AD=CD=BC. Now draw BD. Further, in the Q it is given that CDE is a straight line, that means AB is parallel to CDE. Therefore, we can say that angle ADE is X (alternate angles). Now acc. to second stmt, AE is parallel to BD. Let angle DAE =Z. Consequently, angle ADB =Z (alternate angles). Then angle BDC = Y-Z and angle ABD= Z (because AB=AD). That means X+Z+Z = 180. Therefore, in triangle DAE, angle A = Z and angle D =X. From this, we can calculate that angle AED = Z. This means AD=DE. And therefore because triangle ABD is similar to traingle ADE, BD will also be equal to AE. Thus all sides are equal. And we do not need any specific angle value.

Please help! as to why B cant be the answer. GMAT in two days!!
:cry: :roll:
Math Expert
Joined: 02 Sep 2009
Posts: 94605
Own Kudos [?]: 643489 [1]
Given Kudos: 86734
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
1
Kudos
Expert Reply
noorshergill wrote:

Hi Bunuel,

I think the answer to this Q shd be B. My soln is as follows:

let angle BAD be X, angle ABC be Y. Therefore since ABCD is a rhombus, angle BCD will be X and angle CDA will be Y. Also all the sides are equal of this rhombus, i.e., AB=AD=CD=BC. Now draw BD. Further, in the Q it is given that CDE is a straight line, that means AB is parallel to CDE. Therefore, we can say that angle ADE is X (alternate angles). Now acc. to second stmt, AE is parallel to BD. Let angle DAE =Z. Consequently, angle ADB =Z (alternate angles). Then angle BDC = Y-Z and angle ABD= Z (because AB=AD). That means X+Z+Z = 180. Therefore, in triangle DAE, angle A = Z and angle D =X. From this, we can calculate that angle AED = Z. This means AD=DE. And therefore because triangle ABD is similar to traingle ADE, BD will also be equal to AE. Thus all sides are equal. And we do not need any specific angle value.

Please help! as to why B cant be the answer. GMAT in two days!!
:cry: :roll:


First of all when making such posts please attach a diagram. It's hard to follow all that angles in your explanation.

As for your solution: where did you prove that BD is equal to AB? In rhombus all sides must be equal.
avatar
Intern
Intern
Joined: 26 May 2013
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]
Thanx Bunuel, noticed my error... :P and thanx a ton fr quick reply too :)
User avatar
Manager
Manager
Joined: 26 Sep 2013
Posts: 149
Own Kudos [?]: 624 [0]
Given Kudos: 40
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Send PM
Re: Rhombus [#permalink]
Bunuel wrote:

Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).

So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.

(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.

(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.

Answer: C.


How do you know that BD=AB from 1?? Is there some hidden calculations done in there? All I see is BCD=60, you don't know the measures of any other angles so it doesn't really tell you anything
GMAT Club Bot
Re: Rhombus [#permalink]
 1   2   
Moderator:
Math Expert
94605 posts