GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Sep 2019, 15:50

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

Quadrilateral ABCD is a rhombus and points C, D, and E are

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58142
Re: Rhombus  [#permalink]

Show Tags

New post 16 Dec 2013, 01:06
AccipiterQ wrote:
Bunuel wrote:
Image
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.
_________________
Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 188
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Rhombus  [#permalink]

Show Tags

New post 16 Dec 2013, 12:14
Bunuel wrote:
AccipiterQ wrote:
Bunuel wrote:
Image
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
Manager
Manager
avatar
Joined: 15 Aug 2013
Posts: 229
Re: Rhombus  [#permalink]

Show Tags

New post 11 May 2014, 13:33
Bunuel wrote:
Image
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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58142
Re: Rhombus  [#permalink]

Show Tags

New post 12 May 2014, 02:11
russ9 wrote:
Bunuel wrote:
Image
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.
_________________
Manager
Manager
avatar
Joined: 15 Aug 2013
Posts: 229
Re: Rhombus  [#permalink]

Show Tags

New post 15 May 2014, 17:20
Bunuel wrote:
russ9 wrote:
Bunuel wrote:
Image
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.


Thanks a ton. Very clear now.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2613
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 14 Jul 2015, 07:35
AccipiterQ wrote:
Bunuel wrote:
Image
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.
Manager
Manager
avatar
B
Joined: 10 Mar 2014
Posts: 182
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 05 Aug 2015, 06:49
Bunuel wrote:
russ9 wrote:
Bunuel wrote:
Image
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.

Thanks
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2613
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 05 Aug 2015, 07:02
PathFinder007 wrote:

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


Any quadrilateral with 2 pairs of parallel lines is a parallelogram. All shapes such as rectangles, rhombuses, squares are parallelograms
Retired Moderator
User avatar
S
Joined: 18 Sep 2014
Posts: 1096
Location: India
GMAT ToolKit User Reviews Badge
Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 27 Sep 2015, 02:11
2
Here is my solution for answer C.

Image
Image
Image
Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 704
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 19 Apr 2017, 17:01
http://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.
Senior Manager
Senior Manager
avatar
G
Joined: 09 Feb 2015
Posts: 334
Location: India
Concentration: Social Entrepreneurship, General Management
Schools: Booth '21 (D)
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Reviews Badge
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 19 Apr 2017, 23:34
Bunuel wrote:
Image
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?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58142
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 19 Apr 2017, 23:43
goforgmat wrote:
Bunuel wrote:
Image
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?


Are you talking about the first statement? If yes, then from (1) we k ow that BCD and ABD are equilateral, not ADE.
_________________
Manager
Manager
User avatar
B
Joined: 03 Sep 2018
Posts: 128
CAT Tests
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are  [#permalink]

Show Tags

New post 22 Oct 2018, 00:19
Bunuel wrote:
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. .


Is this a general property, or how do we know that the diagonal BD equals the side of the rhombus?
_________________
Please consider giving Kudos if my post contained a helpful reply or question.
GMAT Club Bot
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are   [#permalink] 22 Oct 2018, 00:19

Go to page   Previous    1   2   [ 33 posts ] 

Display posts from previous: Sort by

Quadrilateral ABCD is a rhombus and points C, D, and E are

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne