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:

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

Because BC=CD, triangle BCD is isosceles. (1) says that angle BCD is 60 degrees, thus triangle BCD is equilateral. Therefore BD=BC=CD.

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

Because BC=CD, triangle BCD is isosceles. (1) says that angle BCD is 60 degrees, thus triangle BCD is equilateral. Therefore BD=BC=CD.

Hope it's clear.

Perfectly, I should have read the question more thoroughly. Thanks

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.

Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.

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.

Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

1. From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

2, Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

3. Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.

1 is correct. 2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral. 3 is correct.
_________________

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.

Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

1. From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

2, Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

3. Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.

1 is correct. 2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral. 3 is correct.

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

Important thing to remember here: Rhombus is a symmetrical quadrilateral wrt the diagonals. What this means is that any diagonal will divide the rhombus into 2 triangles of equal areas. Also, because of the symmetry it is easy to prove that \(\angle A = \angle C\). Additional properties of rhombus are:

•Opposite angles of a rhombus have equal measure. •The two diagonals of a rhombus are perpendicular •Its diagonals bisect opposite angles.

Draw BD to complete triangle ABD. Given, \(\angle {BCD}\) = 60 degrees. ----> \(\angle {BAD}\) = 60 degrees and \(\angle {ABC}\) = \(\angle {CDA}\) = 120 degrees (to complete 360 degree for sum of all internal angles of a quadrilateral).

Now, diagonal BD will bisect \(\angle {CBA}\) and \(\angle {CDA}\) such that \(\angle {ABD} = \angle {ADB}\) = x.

Thus, in triangle ABD, x+x+60 = 180 ----> x = 60 degrees . Thus triangle ABD is equilateral and hence AB = BD.
_________________

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]

Show Tags

05 Aug 2015, 05:49

Bunuel wrote:

russ9 wrote:

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.

Hi Bunuel,

I'm trying to catch my disconnect and tried to explain the reasoning. Appreciate any input.

1. From the question stem, we know that AB=BC=CD=DA because it's a rhombus. We cannot infer the exact degree's besides stating that the opposite angles will be equal and the adjacent will add up to 180. Is that correct to infer?

2, Additionally, we are told/asked "Is quadrilateral ABDE a rhombus?" -- It does say that ABDE is a quadrilateral, meaning, that the lines AE and BD should be parallel and AB and DE should be parallel. Is that correct to infer? I'm guessing the answer is NO. Maybe i'm confusing quadrilateral with parallelogram?

Now, according to statement A = If I know that BCD is 60 degrees, I can automatically infer that BAD is 60 degrees since it's a rhombus. This makes ADE 60 degrees but I don't know anything about the other two angles DAE and DEA.

INSUFFICIENT

3. Additionally, statement two states that (2) AE is parallel to BD. Now I can infer that since AE is parallel to BD and since BA is parallel to DE, it's at least a parallelogram. Correct?

Now, since I know that it's a parallelogram, I can work my way through the angles and realize that it's a parallelogram with all acute angles equal to each other and all obtuse equal to each other. I also know that BC = BD = BA, therefore a Rhombus.

1 is correct. 2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral. 3 is correct.

hi bunuel,

could you please clarify ABDE is a parallelogram (as AE||BD and BA||DE). I just want to know on what basis we are saying ABDE is parallelogram. I am not clear about this.

could you please clarify ABDE is a parallelogram (as AE||BD and BA||DE). I just want to know on what basis we are saying ABDE is parallelogram. I am not clear about this.

Thanks

Any quadrilateral with 2 pairs of parallel lines is a parallelogram. All shapes such as rectangles, rhombuses, squares are parallelograms
_________________

Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]

Show Tags

27 Sep 2015, 01:11

1

This post received KUDOS

Here is my solution for answer C.

_________________

The only time you can lose is when you give up. Try hard and you will suceed. Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources.

Re: Quadrilateral ABCD is a rhombus and points C, D, and E are [#permalink]

Show Tags

28 Nov 2016, 05:00

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.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...