Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 17:36

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
Followers: 5

Kudos [?]: 706 [2] , given: 22

Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

23 Jul 2010, 05:03
2
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

46% (01:31) correct 54% (00:23) wrong based on 377 sessions

### HideShow timer Statistics

Is ABCD a rhombus?

(1) ABCD is a square
(2) ABCD diagonals bisect at 90 degrees
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 447

Kudos [?]: 1978 [1] , given: 210

### Show Tags

23 Jul 2010, 06:23
1
KUDOS

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to $$90^o$$

Statement 2: Diagonals bisect at $$90^o$$

Let's draw a picture to visualize this:
Attachment:

c73058.jpg [ 10.66 KiB | Viewed 4486 times ]
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
$$AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.$$

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at $$90^o$$. Hence it's a rhombus. Sufficient.
Manager
Joined: 04 Oct 2011
Posts: 224
Location: India
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 48 [0], given: 44

### Show Tags

10 Mar 2013, 15:43
whiplash2411 wrote:

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to $$90^o$$

Statement 2: Diagonals bisect at $$90^o$$

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
$$AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.$$

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at $$90^o$$. Hence it's a rhombus. Sufficient.

Hey whiplash2411,
I agree A is Correct choice..
But not D!
I don't think B also leads to solution here..
B just says bisect each other. It doesn't mean that both should be of equal length!

Guys pls correct me if im wrong
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7077

Kudos [?]: 93116 [1] , given: 10552

### Show Tags

10 Mar 2013, 21:43
1
KUDOS
Expert's post
shanmugamgsn wrote:
whiplash2411 wrote:

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to $$90^o$$

Statement 2: Diagonals bisect at $$90^o$$

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
$$AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.$$

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at $$90^o$$. Hence it's a rhombus. Sufficient.

Hey whiplash2411,
I agree A is Correct choice..
But not D!
I don't think B also leads to solution here..
B just says bisect each other. It doesn't mean that both should be of equal length!

Guys pls correct me if im wrong

If the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.
_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 42 [0], given: 17

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

12 Mar 2013, 20:28
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7077

Kudos [?]: 93116 [0], given: 10552

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

13 Mar 2013, 02:37
Expert's post
3
This post was
BOOKMARKED
ziko wrote:
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.

OA is D, not A.

There is a property which says if the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.
_________________
Manager
Joined: 28 Feb 2012
Posts: 115
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 42 [0], given: 17

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

13 Mar 2013, 22:17
Bunuel wrote:
ziko wrote:
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.

OA is D, not A.

There is a property which says if the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.

Most probably i missed the word bisects, which means divides into equal sides, and understood it as intersects. In this case obviously that will be a rombus and no other figure could be drawn. Yes once again i confirm that GMAT has so many small tricky parts.
Thank you Bunuel for clarification.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Manager
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 65
Concentration: Technology, General Management
GMAT 1: 530 Q50 V14
GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 30 [0], given: 60

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

06 Aug 2013, 10:15
All Square are Rombus, so first is that A Satisfies the condition.

Now, if any two diagonals bisects each other, then also it will always be rombus, so B also satisfies the condition.

Since both A and B alone satisfies the condition the answer is D
Intern
Joined: 15 Aug 2011
Posts: 20
Location: United States
Concentration: Marketing, Technology
GPA: 3.6
WE: Project Management (Computer Software)
Followers: 0

Kudos [?]: 15 [0], given: 53

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

06 Aug 2013, 11:06
rxs0005 wrote:
Is ABCD a rhombus?

(1) ABCD is a square
(2) ABCD diagonals bisect at 90 degrees

D

Rule for Rhombus:
Diagonals should bisect each other and angle between diagonals should be 90degrees.
If all sides of a Rhombus are equal then it is a square.

Any square is a Rhombus
If the diagonal bisects at 90 degrees then it is a Rhombus.

So either of the statement alone is sufficient to answer the question.
_________________

"Hit KUDOS if you like my explanation"

Manager
Joined: 10 Mar 2014
Posts: 236
Followers: 1

Kudos [?]: 80 [0], given: 13

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

27 Sep 2014, 10:59
Bunuel wrote:
shanmugamgsn wrote:
whiplash2411 wrote:

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to $$90^o$$

Statement 2: Diagonals bisect at $$90^o$$

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
$$AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.$$

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at $$90^o$$. Hence it's a rhombus. Sufficient.

Hey whiplash2411,
I agree A is Correct choice..
But not D!
I don't think B also leads to solution here..
B just says bisect each other. It doesn't mean that both should be of equal length!

Guys pls correct me if im wrong

If the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.

Hi Bunuel,

I have a query here.

in case of Kite also diagonal are perpendicular bisector. so in st2 cant we consider this as a kite?

Thanks
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1183
Followers: 419

Kudos [?]: 1505 [0], given: 4

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

27 Sep 2014, 11:17
PathFinder007 wrote:

Hi Bunuel,

I have a query here.

in case of Kite also diagonal are perpendicular bisector. so in st2 cant we consider this as a kite?

Thanks

The diagonals of a kite may be perpendicular, but they do not both bisect each other. 'Bisect' means 'cuts perfectly in half', and if you draw a skewed kite, and draw its diagonals, you'll see that one of the two diagonals is not cut perfectly in half at their intersection point.

That said, the question in the original post above is really not the kind of question you see on the GMAT. The GMAT does not test if you know the definition of specialized figures like rhombuses or kites, nor will it test if you know obscure facts about their diagonals.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Director
Joined: 23 Jan 2013
Posts: 579
Schools: Cambridge'16
Followers: 1

Kudos [?]: 42 [0], given: 40

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

15 Oct 2014, 23:43
Never late to study. Bisecting is a trip, eliminating the kite

D
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

20 Oct 2015, 02:56
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.
_________________
Senior Manager
Joined: 17 Jun 2015
Posts: 270
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT 3: Q V
Followers: 3

Kudos [?]: 20 [0], given: 165

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]

### Show Tags

19 Dec 2015, 20:36
Once into parallelograms, there are two types. Imagine two sets.

Set 1: All angles are 90 degrees and only opposite sides are equal
Set 2: All sides are equal but angles are not equal to 90 degrees
Also, a set 3, which is the intersection of these two sets

Set 1 Contains a Rectangle

Set 2 Contains a Rhombus

Set 3, the intersection of the two which has all sides equal as well as all angles equal, is a square.

So.
A square is a rectangle.
But a rectangle is not a square.

A square is a rhombus.
But a rhombus is not a square
Attachments

Screen Shot 2015-12-20 at 10.04.55 AM.png [ 31.42 KiB | Viewed 719 times ]

_________________

Fais de ta vie un rêve et d'un rêve une réalité

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect   [#permalink] 19 Dec 2015, 20:36
Similar topics Replies Last post
Similar
Topics:
1 What is the length of the diagonal of rectangle ABCD? 3 19 May 2016, 23:19
7 Is the quadrilateral ABCD a square? 10 29 Jul 2015, 02:09
3 Is quadrilateral ABCD a square? 3 05 Aug 2014, 09:38
5 What is the area of square ABCD ? 5 13 Sep 2012, 13:06
3 Do the diagonals of a quadrilateral ABCD bisect each other 13 28 Apr 2012, 05:51
Display posts from previous: Sort by