Last visit was: 18 Nov 2025, 19:49 It is currently 18 Nov 2025, 19:49
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
805+ Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,086
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,086
Quadrilateral ABCD is a rhombus and points C, D, and E are 16 Dec 2013, 01:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AccipiterQ
Bunuel

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
Show more

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.
User avatar
AccipiterQ
User avatar
Joined: 26 Sep 2013
Last visit: 03 Sep 2020
Posts: 146
Own Kudos:
715
Given Kudos: 40
Concentration: Finance, Economics
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Schools: HBS '16 (D) Sloan '16 (D) Carroll '16 (WA$) Boston U '16 (A$) Northeastern '16 (A)
GMAT 2: 730 Q49 V41
Posts: 146
Kudos: 715
Quadrilateral ABCD is a rhombus and points C, D, and E are 16 Dec 2013, 12:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
AccipiterQ
Bunuel

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.
Show more


Perfectly, I should have read the question more thoroughly. Thanks
User avatar
russ9
User avatar
Joined: 15 Aug 2013
Last visit: 20 Apr 2015
Posts: 174
Own Kudos:
400
Given Kudos: 23
Posts: 174
Kudos: 400
Quadrilateral ABCD is a rhombus and points C, D, and E are 11 May 2014, 13:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
Show more

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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,086
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,086
Quadrilateral ABCD is a rhombus and points C, D, and E are 12 May 2014, 02:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
russ9
Bunuel

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.
Show more

1 is correct.
2 is not correct. Quadrilateral just means "four sides". So, any four-sided shape is a quadrilateral.
3 is correct.
User avatar
russ9
User avatar
Joined: 15 Aug 2013
Last visit: 20 Apr 2015
Posts: 174
Own Kudos:
400
Given Kudos: 23
Posts: 174
Kudos: 400
Quadrilateral ABCD is a rhombus and points C, D, and E are 15 May 2014, 17:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
russ9
Bunuel

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.
Show more

Thanks a ton. Very clear now.
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,325
Own Kudos:
3,837
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,325
Kudos: 3,837
Quadrilateral ABCD is a rhombus and points C, D, and E are 14 Jul 2015, 07:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AccipiterQ
Bunuel

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
Show more

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.
User avatar
PathFinder007
User avatar
Joined: 10 Mar 2014
Last visit: 21 Oct 2018
Posts: 129
Own Kudos:
733
Given Kudos: 13
Posts: 129
Kudos: 733
Quadrilateral ABCD is a rhombus and points C, D, and E are 05 Aug 2015, 06:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
russ9
Bunuel

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.
Show more

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.

Thanks
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,325
Own Kudos:
3,837
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,325
Kudos: 3,837
Quadrilateral ABCD is a rhombus and points C, D, and E are 05 Aug 2015, 07:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
PathFinder007

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.

Thanks
Show more

Any quadrilateral with 2 pairs of parallel lines is a parallelogram. All shapes such as rectangles, rhombuses, squares are parallelograms
User avatar
Nevernevergiveup
User avatar
Retired Moderator
Joined: 18 Sep 2014
Last visit: 20 Aug 2023
Posts: 1,008
Own Kudos:
3,015
 [4]
Given Kudos: 79
Location: India
Products:
My Reviews
Posts: 1,008
Kudos: 3,015
 [4]
Quadrilateral ABCD is a rhombus and points C, D, and E are 27 Sep 2015, 02:11
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Here is my solution for answer C.



User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 558
Own Kudos:
124
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 558
Kudos: 124
Quadrilateral ABCD is a rhombus and points C, D, and E are 19 Apr 2017, 17:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
https://www.math-prof.com/Geom/Ch_22_Fig_02.jpg I think this picture helps- it clearly explains the structure of a rhombus imo- not all diagrams are created equal (e.x many transversals diagrams show a line decreasing from left to right that intersect two parallel lines but a transversal can also be a right increasing from left to right that cuts through two parallel lines- for some people being shown both diagrams can really help them with spatial awareness). Also, a rhombus is basically an equilateral parallelogram- I find this gives me a much clearer understanding of the relationships between the two figures. From statement 2 we could still have a figure that is a parallelogram, or in other words, only two sides are equal instead of all four. Statement 2 is basically a trap answer/ categorization fallacy the test makers know people are likely to pick.
User avatar
goforgmat
User avatar
Joined: 09 Feb 2015
Last visit: 02 Nov 2019
Posts: 246
Own Kudos:
107
Given Kudos: 232
Location: India
Concentration: Social Entrepreneurship, General Management
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Products:
My Reviews
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 2: 720 Q49 V39
Posts: 246
Kudos: 107
Quadrilateral ABCD is a rhombus and points C, D, and E are 19 Apr 2017, 23:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
Show more

Since we know all angles in triangle ADE is 60 and since one of the sides is AD ,can we not infer that all sides of triangle ADE are equal and hence All sides of Rhombus ABDE are equal.?
What am i missing here?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,086
 [1]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,086
 [1]
Quadrilateral ABCD is a rhombus and points C, D, and E are 19 Apr 2017, 23:43
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
goforgmat
Bunuel

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.

Since we know all angles in triangle ADE is 60 and since one of the sides is AD ,can we not infer that all sides of triangle ADE are equal and hence All sides of Rhombus ABDE are equal.?
What am i missing here?
Show more

Are you talking about the first statement? If yes, then from (1) we k ow that BCD and ABD are equilateral, not ADE.
User avatar
SchruteDwight
User avatar
Joined: 03 Sep 2018
Last visit: 30 Mar 2023
Posts: 167
Own Kudos:
113
Given Kudos: 923
Location: Netherlands
Schools: HEC MiM "22 (S) LBS MiM "21 (A)
GPA: 4
Products:
My Reviews
Schools: HEC MiM "22 (S) LBS MiM "21 (A)
Posts: 167
Kudos: 113
Quadrilateral ABCD is a rhombus and points C, D, and E are 22 Oct 2018, 00:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. .
Show more

Is this a general property, or how do we know that the diagonal BD equals the side of the rhombus?
User avatar
tinytiger
User avatar
Joined: 26 Aug 2017
Last visit: 10 Sep 2025
Posts: 47
Own Kudos:
120
Given Kudos: 695
Location: Singapore
Schools: INSEAD Sept'21 Intake (A$) Wharton '23 (II)
GMAT 1: 710 Q49 V37
GMAT 2: 760 Q50 V44
WE:General Management (Healthcare/Pharmaceuticals)
Products:
My Reviews
Schools: INSEAD Sept'21 Intake (A$) Wharton '23 (II)
GMAT 2: 760 Q50 V44
Posts: 47
Kudos: 120
Quadrilateral ABCD is a rhombus and points C, D, and E are 02 Jun 2020, 08:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For (2), we can look at it in terms of the properties of a rhombus by selecting only 2 more easily comparable shapes of a rhombus:

a) If ABCD comprises of 2 equilateral triangles, then AE // to BD would automatically make ABDE a rhombus. This is the easy shape that most of us can imagine to be sufficient.

b) However, if ABCD = a square (remember that a square is a special type of rhombus where its angles are at 90* and diagonals are congruent), we know that BD is obviously greater than any side of ABCD:
- AB=BC=CD=DA = x, then BD = Rt2 (x).
- Since BD // AE where AB and CDE are // straight lines, then we know BD = AE = Rt2 (X) which is > than AD = DE = X.

So how can ABDE definitely only be a rhombus in the second case? Not sufficient.
User avatar
D4kshGargas
User avatar
Joined: 01 Apr 2020
Last visit: 28 Feb 2021
Posts: 86
Own Kudos:
32
Given Kudos: 282
Location: India
GMAT 1: 650 Q46 V34 (Online)
GMAT 2: 680 Q48 V35 (Online)
GMAT 2: 680 Q48 V35 (Online)
Posts: 86
Kudos: 32
Quadrilateral ABCD is a rhombus and points C, D, and E are 29 Jun 2020, 06:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

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.
Show more

Hi,
I don't seem to find any such property for Rhombus on the internet.
Can you please confirm?
Thanks!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,086
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,086
Quadrilateral ABCD is a rhombus and points C, D, and E are 29 Jun 2020, 06:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
D4kshGargas
Bunuel

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,
I don't seem to find any such property for Rhombus on the internet.
Can you please confirm?
Thanks!
Show more

This is not a property. This is true because we are given that (1) The measure of angle BCD is 60 degrees.

BTW, this is already explained in this thread. Please read the whole thread before posting a question.
User avatar
D4kshGargas
User avatar
Joined: 01 Apr 2020
Last visit: 28 Feb 2021
Posts: 86
Own Kudos:
32
Given Kudos: 282
Location: India
GMAT 1: 650 Q46 V34 (Online)
GMAT 2: 680 Q48 V35 (Online)
GMAT 2: 680 Q48 V35 (Online)
Posts: 86
Kudos: 32
Quadrilateral ABCD is a rhombus and points C, D, and E are 29 Jun 2020, 06:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
D4kshGargas
Bunuel

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,
I don't seem to find any such property for Rhombus on the internet.
Can you please confirm?
Thanks!

This is not a property. This is true because we are given that (1) The measure of angle BCD is 60 degrees.

BTW, this is already explained in this thread. Please read the whole thread before posting a question.
Show more

Sorry, my bad!
I didn't move to Page 2
I'll take care in the future!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
Quadrilateral ABCD is a rhombus and points C, D, and E are 13 Feb 2023, 02:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
   1   2 
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts