Last visit was: 18 Nov 2025, 18:37 It is currently 18 Nov 2025, 18:37
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 
655-705 Level|   Geometry|      
User avatar
amanvermagmat
User avatar
Retired Moderator
Joined: 22 Aug 2013
Last visit: 28 Mar 2025
Posts: 1,148
Own Kudos:
2,854
Given Kudos: 480
Location: India
Posts: 1,148
Kudos: 2,854
Is quadrilateral ABCD a rhombus? 18 Jun 2018, 20:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
manishk30
Bunuel
Thought about this again: D it is.

Well:
(1) True for square or for rhombus but every square is a rhombus, so sufficient
(2) Again true for square or for rhombus but every square is a rhombus, so sufficient

D


Just one question if you could help me.
Are not diagonals of rectangle perpendicular bisectors of each other. I know that they are not equal but they are at 90 degrees to each other and divide the diagonals in equal halves.
Show more

Hello

Diagonals of a rectangle ARE EQUAL and ARE bisectors of each other, but they are NOT necessarily perpendicular bisectors.
A rectangle in which diagonals intersect at perpendicular (90 degrees) becomes a square
avatar
mrjoe1
avatar
Joined: 21 Sep 2018
Last visit: 25 Nov 2018
Posts: 1
Given Kudos: 32
Posts: 1
Kudos: 0
Is quadrilateral ABCD a rhombus? 01 Nov 2018, 07:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Thought about this again: D it is.

Well:
(1) True for square or for rhombus but every square is a rhombus, so sufficient
(2) Again true for square or for rhombus but every square is a rhombus, so sufficient

D
Show more

Bunuel, following your logic, is it true that every rectangle is parallelogram?

also if I have a square this means that it is also a rectangle, a rhombus and a parallelogram, right?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,078
 [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: 778,078
 [1]
Is quadrilateral ABCD a rhombus? 01 Nov 2018, 07:18
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mrjoe1
Bunuel
Thought about this again: D it is.

Well:
(1) True for square or for rhombus but every square is a rhombus, so sufficient
(2) Again true for square or for rhombus but every square is a rhombus, so sufficient

D

Bunuel, following your logic, is it true that every rectangle is parallelogram?

also if I have a square this means that it is also a rectangle, a rhombus and a parallelogram, right?
Show more
_________________
Correct and correct.
User avatar
CEdward
User avatar
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,203
Own Kudos:
272
Given Kudos: 332
Posts: 1,203
Kudos: 272
Is quadrilateral ABCD a rhombus? 21 Mar 2021, 13:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
mk87
Hi guys
I'm a little confused as to whether we should consider the properties of a kite when dealing with quadrilaterals. For example:

Is quadrilateral ABCD a Rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other
(2) AB = BC = CD = AD

The official answer is as follows:
Statement 1 - SUFFICIENT: The diagonals of a rhombus are perpendicular bisectors of one another. This is in fact enough information to prove that a quadrilateral is a rhombus
Statement 2 - A quadrilateral with four equal sides is by definition a rhombus

What I don't get is that the question mentions it is a quadrilateral, not a parallelogram. In this case, how can we eliminate the possibility that it could be a kite as well in Statement 1?

Statement 1 says the diagonals are perpendicular bisectors of each other which means that they intersect each other at mid points and form 90 degree angles. It is not possible that they are in the shape of an asymmetric kite. Figure 1 is not possible. Only figure 2 is possible. In figure 2, all sides will be equal.
Attachment:
Ques4.jpg
Show more

This is an interesting post. So to be clear, the distinction is this

1. The diagonals of a kite INTERSECT each other, but we don't consider them as bisectors b/c the diagonals are not split evenly
2. The diagonals of a rhombus are PERPENDICULAR BISECTORS (bisection b/c diagonals are split evenly into two)
3. The diagonals of a rectangle are NON-PERPENDICULAR bisectors (b/c the bisection does not form 90 degree angles), but in the case of a square the bisectors ARE perpendicular bisectors.

Bunuel is this accurate?
User avatar
MBAB123
User avatar
Joined: 05 Jul 2020
Last visit: 30 Jul 2023
Posts: 563
Own Kudos:
318
Given Kudos: 151
GMAT 1: 720 Q49 V38
WE:Accounting (Accounting)
Products:
My Reviews
GMAT 1: 720 Q49 V38
Posts: 563
Kudos: 318
Is quadrilateral ABCD a rhombus? 28 Jul 2021, 05:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CEdward
VeritasKarishma
mk87
Hi guys
I'm a little confused as to whether we should consider the properties of a kite when dealing with quadrilaterals. For example:

Is quadrilateral ABCD a Rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other
(2) AB = BC = CD = AD

The official answer is as follows:
Statement 1 - SUFFICIENT: The diagonals of a rhombus are perpendicular bisectors of one another. This is in fact enough information to prove that a quadrilateral is a rhombus
Statement 2 - A quadrilateral with four equal sides is by definition a rhombus

What I don't get is that the question mentions it is a quadrilateral, not a parallelogram. In this case, how can we eliminate the possibility that it could be a kite as well in Statement 1?

Statement 1 says the diagonals are perpendicular bisectors of each other which means that they intersect each other at mid points and form 90 degree angles. It is not possible that they are in the shape of an asymmetric kite. Figure 1 is not possible. Only figure 2 is possible. In figure 2, all sides will be equal.
Attachment:
Ques4.jpg

This is an interesting post. So to be clear, the distinction is this

1. The diagonals of a kite INTERSECT each other, but we don't consider them as bisectors b/c the diagonals are not split evenly
2. The diagonals of a rhombus are PERPENDICULAR BISECTORS (bisection b/c diagonals are split evenly into two)
3. The diagonals of a rectangle are NON-PERPENDICULAR bisectors (b/c the bisection does not form 90 degree angles), but in the case of a square the bisectors ARE perpendicular bisectors.

Bunuel is this accurate?
Show more

CEdward - this link is pretty awesome for quadrilaterals - https://e-gmat.com/blogs/quadrilateral-properties-formulas-rectangle-square-parallelogram-rhombus-trapezium-trapezoid/
avatar
amoghhlgr
avatar
Joined: 16 Jun 2019
Last visit: 19 Jul 2023
Posts: 28
Own Kudos:
9
Given Kudos: 135
Location: India
Schools: Said'16
GMAT 1: 690 Q44 V40
GPA: 3.5
Schools: Said'16
GMAT 1: 690 Q44 V40
Posts: 28
Kudos: 9
Is quadrilateral ABCD a rhombus? 04 Dec 2021, 01:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Thought about this again: D it is.

Well:
(1) True for square or for rhombus but every square is a rhombus, so sufficient
(2) Again true for square or for rhombus but every square is a rhombus, so sufficient

D
Show more

What about the kite? It has a perpendicular bisector, so 1 is out??
avatar
shalin23
avatar
Joined: 27 Aug 2021
Last visit: 21 Jan 2022
Posts: 11
Given Kudos: 27
Location: India
Posts: 11
Kudos: 0
Is quadrilateral ABCD a rhombus? 21 Dec 2021, 06:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am kind of confused because, in previous DS questions, the answers probably would be E for such a question.

I feel the inference is kind of vague.


According to statement 1, cant the figure be both a Square and a Rhombus?

Same for statement 2...

Can someone please clarify how to infer here thanks.
User avatar
RastogiSarthak99
User avatar
Joined: 20 Mar 2019
Last visit: 10 Aug 2024
Posts: 141
Own Kudos:
23
Given Kudos: 282
Location: India
Posts: 141
Kudos: 23
Is quadrilateral ABCD a rhombus? 15 Jun 2022, 07:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think the most important thing to understand here is that every square is a rhombus
User avatar
prachisaraf
User avatar
Joined: 03 Jan 2023
Last visit: 31 Jul 2023
Posts: 28
Own Kudos:
4
Given Kudos: 299
Posts: 28
Kudos: 4
Is quadrilateral ABCD a rhombus? 10 Mar 2023, 11:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Economist
Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD
Show more

Is it true that square is a kind of rhombus ? Aren't the properties different for both wrt diagonals length ? Can we assume this for all questions where it can be either a square or a rhombus ?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,078
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: 778,078
Is quadrilateral ABCD a rhombus? 10 Mar 2023, 11:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
prachisaraf
Economist
Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD

Is it true that square is a kind of rhombus ? Aren't the properties different for both wrt diagonals length ? Can we assume this for all questions where it can be either a square or a rhombus ?
Show more

Every square is a rhombus, but every rhombus is not a square.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
Is quadrilateral ABCD a rhombus? 27 Aug 2025, 20:01
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