Find all School-related info fast with the new School-Specific MBA Forum

It is currently 04 Sep 2015, 20:11
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is quadrilateral ABCD a rhombus?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 903
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 18

Kudos [?]: 364 [0], given: 18

Is quadrilateral ABCD a rhombus? [#permalink] New post 14 Oct 2009, 20:09
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

33% (01:37) correct 67% (00:39) wrong based on 308 sessions
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD
[Reveal] Spoiler: OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50376 [0], given: 7544

Re: rhombus? [#permalink] New post 14 Oct 2009, 20:40
Expert's post
2
This post was
BOOKMARKED
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50376 [0], given: 7544

Re: rhombus? [#permalink] New post 14 Oct 2009, 20:45
Expert's post
1
This post was
BOOKMARKED
Senior Manager
Senior Manager
avatar
Joined: 17 May 2010
Posts: 300
GMAT 1: 710 Q47 V40
Followers: 4

Kudos [?]: 38 [0], given: 7

Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink] New post 16 Jun 2011, 14:24
1
This post was
BOOKMARKED
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

Solve!
_________________

If you like my post, consider giving me KUDOS!

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 759
Followers: 14

Kudos [?]: 75 [0], given: 42

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 17 Jun 2011, 17:45
1. Sufficient

diagnols are perpendicular bisectors. can only happen in a square or rhombus. Square is a kind of rhombus.

2. Sufficient

As we know its a square or rhombus. Square is a kind of rhombus.

Answer is D.
Intern
Intern
avatar
Joined: 16 Aug 2011
Posts: 12
Concentration: Finance, Entrepreneurship
GPA: 3.51
Followers: 0

Kudos [?]: 32 [0], given: 3

Rhombus Vs. Kite [#permalink] New post 10 Nov 2011, 00:16
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?
_________________

+1 Kudos is a great way of saying Thank you!! :D

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5870
Location: Pune, India
Followers: 1485

Kudos [?]: 8016 [0], given: 190

Re: Rhombus Vs. Kite [#permalink] New post 10 Nov 2011, 02:54
Expert's post
1
This post was
BOOKMARKED
mk87 wrote:
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
Ques4.jpg [ 10.18 KiB | Viewed 1767 times ]

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 294 [0], given: 11

GMAT ToolKit User
Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink] New post 29 Jan 2013, 06:59
gijoedude wrote:
Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD



A rhombus is a quadrilateral with all its sides equal to each other.

1.
Imagine that the point where the bisectors meet is called X.
Then, BX = DX and AX = CX.

Using the Pythagorean Theorem you could imagine getting the hypotenuse of sides BX and CX.
Since AX = CX, then the hypotenuse of BX and AX is also as long as the previous.
As you could imagine, all the hypotenuse formed are equal, thus forming equal 4 sides. Hence, a rhombus.

SUFFICIENT.

2.

All sides are equal.

SUFFICIENT.

Answer: D
_________________

Impossible is nothing to God.

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 346 [0], given: 355

GMAT ToolKit User
Re: rhombus? [#permalink] New post 13 Oct 2013, 15:10
Bunuel wrote:
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

Hi Bunuel

When they perpendicular bisectors they mean that all angles and all sides are equal, therefore it is a square. And a square is just a type of rhombus?

And for statement 2, when they say that all sides are equal, you can assume that it is a square therefore it is also a rhombus?

Is that the correct line of reasoning?
Thanks so much in advance
Cheers
J :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50376 [0], given: 7544

Re: rhombus? [#permalink] New post 13 Oct 2013, 15:20
Expert's post
jlgdr wrote:
Bunuel wrote:
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

Hi Bunuel

When they perpendicular bisectors they mean that all angles and all sides are equal, therefore it is a square. And a square is just a type of rhombus?

And for statement 2, when they say that all sides are equal, you can assume that it is a square therefore it is also a rhombus?

Is that the correct line of reasoning?
Thanks so much in advance
Cheers
J :)


For (1): a perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

Thus, "line segments AC and BD are perpendicular bisectors of each other" means that AC cuts BD into two equal parts at 90° and BD cuts AC into two equal parts at 90°.

For (2): AB = BC = CD = AD, means that ABCD is either a rhombus or square (so still a rhombus).

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 475
Followers: 1

Kudos [?]: 93 [0], given: 134

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 06 Dec 2013, 10:10
Is quadrilateral ABCD a rhombus?

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

But doesn't a rhombus also allow for two perpendicular bisectors? A square has two perpendicular bisectors but a square is not a rhombus (because a rhombus does not have all four angles = 90. Oh, but wait, a rhombus is a square in the same way a rectangle is a square but not the other way around. Tricky.

(2) AB = BC = CD = AD

I guess the same logic applies above, ABCD could be a square or rhombus but regardless of which one it is its still a rhombus. If the stem asked if ABCD was a square, then this would be insufficient.
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 231
Followers: 5

Kudos [?]: 69 [0], given: 148

GMAT ToolKit User
Re: Data Sufficiency - doubts [#permalink] New post 08 Aug 2014, 20:36
kritim22 wrote:
Hi,

can someone help me with this question please:

Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

The answer it says is D- each statement is enough on its own.

Doubt- can't these properties also apply to a square? How can we confirm it's a rhombus?


Let say AC and BD meet at O. We have OD= OB, OA= OC. If you use pithagoras theorem, you can easily see that AD= DC=BC=AB.
For example, AD^2= OA^2 + OD^2
So (1) and (2) basically say the same thing.
The definition of rhombus is a quadrilateral whose four sides have the same length. So D is the answer.
_________________

.........................................................................
+1 Kudos please, if you like my post

Manager
Manager
avatar
Joined: 21 Sep 2012
Posts: 153
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Followers: 1

Kudos [?]: 97 [0], given: 31

Re: Data Sufficiency - doubts [#permalink] New post 08 Aug 2014, 23:56
kritim22 wrote:
Hi,

can someone help me with this question please:

Is quadrilateral ABCD a rhombus?

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

(2) AB = BC = CD = AD

The answer it says is D- each statement is enough on its own.

Doubt- can't these properties also apply to a square? How can we confirm it's a rhombus?


A square is a special case of rhombus. It has all angles of 90 degrees. so proving that quadrilateral ABCD is a square is sufficient to say that it is a rhombus.
Director
Director
User avatar
Joined: 17 Apr 2013
Posts: 636
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Followers: 18

Kudos [?]: 155 [0], given: 284

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 05 Nov 2014, 02:31
Bunuel wrote:
Answer D.

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

(2) AB = BC = CD = AD --> rhombus

Or am I missing something, seems pretty obvious...



But Bunuel this would be true even for rectangle:
Line segments AC and BD are perpendicular bisectors of each other.

I need Your though, am confused. Diagonals of rectangles also bisect each other.
_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: how-to-score-750-and-750-i-moved-from-710-to-189016.html

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50376 [0], given: 7544

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 05 Nov 2014, 04:09
Expert's post
honchos wrote:
Bunuel wrote:
Answer D.

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

(2) AB = BC = CD = AD --> rhombus

Or am I missing something, seems pretty obvious...



But Bunuel this would be true even for rectangle:
Line segments AC and BD are perpendicular bisectors of each other.

I need Your though, am confused. Diagonals of rectangles also bisect each other.


For (1): a perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

Thus, "line segments AC and BD are perpendicular bisectors of each other" means that AC cuts BD into two equal parts at 90° and BD cuts AC into two equal parts at 90°.

Now, the diagonals of a rectangle, though cut each other into two equal parts, do NOT necessarily cut each other at 90°. This happens only if a rectangle is a square but if ABCD is a square then it's also a rhombus.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 10 Sep 2014
Posts: 75
Followers: 0

Kudos [?]: 36 [0], given: 102

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 06 Nov 2014, 01:17
Bunuel,

For (1), can you consider the case of a kite?

Bunuel wrote:
honchos wrote:
Bunuel wrote:
Answer D.

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

(2) AB = BC = CD = AD --> rhombus

Or am I missing something, seems pretty obvious...



But Bunuel this would be true even for rectangle:
Line segments AC and BD are perpendicular bisectors of each other.

I need Your though, am confused. Diagonals of rectangles also bisect each other.


For (1): a perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

Thus, "line segments AC and BD are perpendicular bisectors of each other" means that AC cuts BD into two equal parts at 90° and BD cuts AC into two equal parts at 90°.

Now, the diagonals of a rectangle, though cut each other into two equal parts, do NOT necessarily cut each other at 90°. This happens only if a rectangle is a square but if ABCD is a square then it's also a rhombus.

Hope it's clear.

_________________

Press KUDOs if you find my explanation helpful

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4755

Kudos [?]: 50376 [0], given: 7544

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 06 Nov 2014, 06:22
Expert's post
Senior Manager
Senior Manager
User avatar
Joined: 10 Mar 2013
Posts: 264
Followers: 1

Kudos [?]: 37 [0], given: 2211

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 10 Mar 2015, 19:32
This question is poor, because (1) could be right kite, which is not necessarily a rhombus or a rhombus, but (2) will always satisfy a rhombus.
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5870
Location: Pune, India
Followers: 1485

Kudos [?]: 8016 [1] , given: 190

Re: Is quadrilateral ABCD a rhombus? [#permalink] New post 10 Mar 2015, 21:58
1
This post received
KUDOS
Expert's post
TooLong150 wrote:
This question is poor, because (1) could be right kite, which is not necessarily a rhombus or a rhombus, but (2) will always satisfy a rhombus.


Actually, the question is fine.

A rhombus is a quadrilateral all of whose sides are of the same length - that's all. You could have a rhombus which also has all angles 90 which makes it a square or a rhombus in the shape of a kite. But nevertheless, if it is a quadrilateral and has all sides equal, it IS A RHOMBUS.

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

Make 2 lines - a vertical and a horizontal - which are perpendicular bisectors of each other. Make them in any way of any length - just that they should be perpendicular bisectors of each other. When you join the end points, you will get all sides equal. Think of it this way - each side you get will be a hypotenuse of a right triangle. The legs of the right triangle will have the same pair of lengths in all 4 cases. So AB = BC = CD = AD. So ABCD must be a rhombus.

(2) AB = BC = CD = AD

This statement directly tells you that all sides are equal so ABCD must be a rhombus.

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 22 Aug 2015
Posts: 1
Followers: 0

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

Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD [#permalink] New post 22 Aug 2015, 10:10
While somewhat unusual, isn't the fact that it asks if the quadrilateral is a rhombus sufficient in itself? Aren't all quadrilaterals also rhombuses and vise versa because they have 4 sides?
Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD   [#permalink] 22 Aug 2015, 10:10

Go to page    1   2    Next  [ 24 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Is quadrilateral ABCD a rhombus? honchos 2 20 Dec 2014, 01:30
Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD gijoedude 0 22 Aug 2015, 13:28
1 Experts publish their posts in the topic ABCD is a quadrilateral. A rhombus is a quadrilateral whose burp 14 29 Dec 2010, 07:08
5 Experts publish their posts in the topic Quadrilateral ABCD is a rhombus and points C, D, and E are vscid 3 09 Mar 2010, 19:10
28 Experts publish their posts in the topic Quadrilateral ABCD is a rhombus and points C, D, and E are crejoc 27 09 Aug 2009, 09:03
Display posts from previous: Sort by

Is quadrilateral ABCD a rhombus?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.