NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 20:28 It is currently 23 Apr 2024, 20:28
Decision Tracker
My Rewards
New posts
New comers' posts

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

Is the quadrilateral a square?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
enigma123
Senior Manager
Senior Manager
Joined: 25 Jun 2011
Status:Finally Done. Admitted in Kellogg for 2015 intake
Posts: 396
Own Kudos [?]: 16644 [18]
Given Kudos: 217
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE:Information Technology (Consulting)
Send PM
Is the quadrilateral a square? [#permalink] New post   Updated on: 14 Sep 2019, 05:32
2
Kudos
16
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

75% (00:30) correct 25% (00:39) wrong based on 566 sessions
Hide Show timer Statistics
Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 17487 times ]
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

Show Spoiler
In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?
ShowHide Answer
Official Answer
C

Originally posted by enigma123 on 11 Feb 2012, 14:08.
Last edited by Bunuel on 14 Sep 2019, 05:32, edited 3 times in total.
Edited the question
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618618 [9]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Is the quadrilateral a square? [#permalink] New post   11 Feb 2012, 14:48
3
Kudos
6
Bookmarks
Expert Reply
Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 17399 times ]
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA --> both square and rhombus have all four sides equal in length. Not sufficient.

(2) AC = BD --> both square and rectangle have diagonals equal in length. Not sufficient.

(1)+(2) ABCD is a square. Sufficient.

Answer: C.

Useful property: if the diagonals of a rhombus are equal, then that rhombus must be a square. So you can apply this for (1)+(2) and conclude that ABCD must be a square.

Check Polygons chapter of Math Book for more useful properties and tips: math-polygons-87336.html

Hope it helps.
General Discussion
avatar
madn800
Manager
Manager
Joined: 07 May 2013
Posts: 67
Own Kudos [?]: 60 [1]
Given Kudos: 1
Send PM
Re: Is the quadrilateral a square? [#permalink] New post   05 Aug 2013, 19:07
1
Kudos
from 1 it is clear that it is either a rhombus or a square as all sides are equal.

from 2 it is established that it is a square as IN A RHOMBUS DIAGONALS ARE NOT EQUAL.

hence C.
avatar
Asifpirlo
Manager
Manager
Joined: 10 Jul 2013
Posts: 229
Own Kudos [?]: 1036 [1]
Given Kudos: 102
Send PM
Re: Is the quadrilateral a square? [#permalink] New post   05 Aug 2013, 23:08
1
Kudos
enigma123 wrote:
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?



square has equal sides and equal diagonals.
rhombus has equal sides but not equal diagonals.
so both together are sufficient...... Answer (C)

About the 2nd question, let p the point of intersection ofthe two diagonal AC and BD.
now angle PAB = angle PBA [because PA=PB]
so angle APB has to be 90 or it will not be possible for the total angle surrounding the point P to be 360.
so diagonals have to bisect at 90 degress
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11161
Own Kudos [?]: 31870 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: Is the quadrilateral a square? [#permalink] New post   24 Jul 2015, 02:23
Expert Reply
divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD



Hi,
1) statement tells us all sides are equal. it could be a rhombus , a square etc.... insuff
2) stat 2 tells us that the diagonals are equal.. it could be a rectangle , a square or any other quad.. insuff

combined we know it can only be a square... suff
avatar
divyarathi15
Intern
Intern
Joined: 16 Jan 2015
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 4
Send PM
Re: Is the quadrilateral a square? [#permalink] New post   24 Jul 2015, 02:32
Hi!

We could also say from statement 1 that it could be any irregular quadrilateral (apart from being either a rhombus/sq). Again from statement 2 it can be concluded that the figure could be any irregular quad too. combining both cant it be concluded that the figure could be an irregular quadrilateral too?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618618 [4]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Is the quadrilateral a square? [#permalink] New post   24 Jul 2015, 02:40
4
Bookmarks
Expert Reply
divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD


Similar questions to practice:
is-quadrilateral-abcd-a-rectangle-156161.html
is-quadrilateral-rstv-a-rectangle-130928.html
is-quadrilateral-abcd-a-rectangle-100729.html
is-quadrilateral-abcd-a-rectangle-89598.html
is-quadrilateral-abcd-a-rhombus-85336.html
is-quadrilateral-mnpq-a-rectangle-173764.html
quadrilateral-abcd-is-a-rhombus-and-points-c-d-and-e-are-82126.html
if-a-b-and-c-are-distinct-points-135308.html
is-the-quadrilateral-a-square-127383.html
is-quadrilateral-abcd-a-rectangle-199396.html
in-the-quadrilateral-abcd-side-ad-is-parallel-to-side-bc-119608.html
is-quadrilateral-abcd-a-parallelogram-188759.html
is-abcd-rectangular-156356.html
is-abcd-a-rombus-1-abcd-is-a-square-2-abcd-diagonals-bisect-97819.html
if-abcd-is-a-quadrilateral-is-ab-bc-cd-da-100359.html
is-the-quadrilateral-abcd-a-square-202502.html

Hope it helps.
avatar
S
harikrish
Manager
Manager
Joined: 05 Nov 2014
Posts: 79
Own Kudos [?]: 83 [0]
Given Kudos: 113
Location: India
Concentration: Strategy, Operations
Schools: Stanford '20 ISB '19 IIM-A"19
GMAT 1: 580 Q49 V21
GPA: 3.75
Send PM
Reviews Badge
Re: Is the quadrilateral a square? [#permalink] New post   22 Jun 2017, 08:07
enigma123 wrote:
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?


Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.
User avatar
B
longhaul123
Manager
Manager
Joined: 03 Jul 2017
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Posts: 147
Own Kudos [?]: 33 [0]
Given Kudos: 27
Location: India
Concentration: Finance, International Business
Send PM
Re: Is the quadrilateral a square? [#permalink] New post   27 Jul 2017, 21:42
I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombus or a square or a rectangle.
1 and 2 together C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618618 [0]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Is the quadrilateral a square? [#permalink] New post   27 Jul 2017, 21:47
Expert Reply
longhaul123 wrote:
I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombusor a square or a rectangle.
1 and 2 together C


A rhombus with equal diagonal is a square.
User avatar
L
GMATBusters
GMAT Tutor
Joined: 27 Oct 2017
Posts: 1907
Own Kudos [?]: 5578 [0]
Given Kudos: 236
WE:General Management (Education)
Send PM
GMAT ToolKit User
Re: Is the quadrilateral a square? [#permalink] New post   14 May 2018, 07:06
Expert Reply
Statement 2: It can be either a square or a rectangle or any equidiagonal quadrilateral
Quadrilaterals with equal diagonal are called equidiagonal quadrilateral.
Attachment:
Equidiagonal Quandrilateral.jpg
Equidiagonal Quandrilateral.jpg [ 36.68 KiB | Viewed 11759 times ]



harikrish wrote:
enigma123 wrote:
Attachment:
The attachment ABCD.png is no longer available
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?


Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle or any equidiagonal quadrilateral.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32633
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Is the quadrilateral a square? [#permalink] New post   27 Dec 2023, 03:21
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.
GMAT Club Bot
gmatclubot
Re: Is the quadrilateral a square? [#permalink]
27 Dec 2023, 03:21
Moderator:
Bunuel
Math Expert
92883 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions