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

It is currently 25 Jun 2016, 16:21
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 rectangle?

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

Hide Tags

Manager
Manager
avatar
Joined: 17 Nov 2009
Posts: 239
Followers: 1

Kudos [?]: 29 [0], given: 17

Is quadrilateral ABCD a rectangle? [#permalink]

Show Tags

New post 09 Sep 2010, 07:42
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (01:32) correct 42% (00:38) wrong based on 173 sessions

HideShow timer Statistics

Is quadrilateral ABCD a rectangle?

(1) Angle ABC = 90 degrees
(2) AB = CD
[Reveal] Spoiler: OA
Senior Manager
Senior Manager
avatar
Joined: 06 Jun 2009
Posts: 333
Location: USA
WE 1: Engineering
Followers: 1

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

Re: Rectangles [#permalink]

Show Tags

New post 09 Sep 2010, 07:59
agnok wrote:
Is quadrilateral ABCD a rectangle?

1. angle ABC = 90 degrees
2. AB=CD

Please explain your solution.


E

1. ABC = 90 ................ other angles can be of any value.

2. AB = CD ............... AC and BD might not be equal.

For rectangle, all angles have to be equal (hence, 90) and opposite sides should be equal. Neither of the two statement helps in determining if the two requirements are satisfied or not.
_________________

All things are possible to those who believe.

Senior Manager
Senior Manager
avatar
Joined: 20 Jul 2010
Posts: 269
Followers: 2

Kudos [?]: 62 [0], given: 9

GMAT ToolKit User Reviews Badge
Re: Rectangles [#permalink]

Show Tags

New post 09 Sep 2010, 08:08
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1712
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 85

Kudos [?]: 719 [0], given: 109

Re: Rectangles [#permalink]

Show Tags

New post 09 Sep 2010, 08:18
E

It may be a square.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33499
Followers: 5928

Kudos [?]: 73443 [0], given: 9902

Re: Rectangles [#permalink]

Show Tags

New post 09 Sep 2010, 09:02
Expert's post
agnok wrote:
Is quadrilateral ABCD a rectangle?

1. angle ABC = 90 degrees
2. AB=CD

Please explain your solution.


A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:
rectangle.PNG
rectangle.PNG [ 4.39 KiB | Viewed 3542 times ]
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.


It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 17 Nov 2009
Posts: 239
Followers: 1

Kudos [?]: 29 [0], given: 17

Re: Rectangles [#permalink]

Show Tags

New post 09 Sep 2010, 12:07
The diagram made the difference in understanding the answer.. thanks
Senior Manager
Senior Manager
avatar
Joined: 20 Jul 2010
Posts: 269
Followers: 2

Kudos [?]: 62 [0], given: 9

GMAT ToolKit User Reviews Badge
Re: Rectangles [#permalink]

Show Tags

New post 12 Sep 2010, 09:59
Thanks Bunuel for the diagram
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 233
Followers: 1

Kudos [?]: 58 [0], given: 13

Premium Member
Re: Rectangles [#permalink]

Show Tags

New post 18 Apr 2014, 04:02
Bunuel wrote:
agnok wrote:
Is quadrilateral ABCD a rectangle?

1. angle ABC = 90 degrees
2. AB=CD

Please explain your solution.


A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:
rectangle.PNG
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.


It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.


HI Bunnel,

One doubt. Here it is mentioned that angle ABC are 90 degrees. and quadrilateral have total of 360 degree. so fourth one should be 90 degree.

then why you have mentioned following statement.

angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient

Thanks
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33499
Followers: 5928

Kudos [?]: 73443 [0], given: 9902

Re: Rectangles [#permalink]

Show Tags

New post 18 Apr 2014, 04:32
Expert's post
PathFinder007 wrote:
Bunuel wrote:
agnok wrote:
Is quadrilateral ABCD a rectangle?

1. angle ABC = 90 degrees
2. AB=CD

Please explain your solution.


A rectangle is a quadrilateral with four right angles - this is necessary and sufficient condition for quadrilateral to be a rectangle.

(1) angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient.
(2) AB=CD --> opposite sides AB and CD are equal, clearly insufficient.

(1)+(2) Look at the diagram:
Attachment:
rectangle.PNG
It's possible quadrilateral to be a rectangle (case ABCD1) and it's also possible quadrilateral not to be a rectangle (case ABCD2). Not sufficient.

saxenashobhit wrote:
E

for rectangle = all have to be 90 and opp sides equal
1. ABC= 90 : dont know about other angles - insuff
2. AB= CD , other sides may or may not be equal - insuff

together - not necessarily a rectangle, may be a square - insuff
Ans is E

metallicafan wrote:
E

It may be a square.


It's not necessary ABCD to be square (look at the diagram, it can be simple rectangle). In fact if we knew that ABCD is a square then statements would be sufficient, because square is a special type of rectangle, which means that every square is a rectangle (but not vise-versa).

Hope it helps.


HI Bunnel,

One doubt. Here it is mentioned that angle ABC are 90 degrees. and quadrilateral have total of 360 degree. so fourth one should be 90 degree.

then why you have mentioned following statement.

angle ABC = 90 degrees --> we know nothing about other angles. Not sufficient

Thanks


Yes, the Sum of Interior Angles of a polygon is \(180(n-2)\) degrees, where \(n\) is the number of sides (so is the number of angles). Thus the sum of the interior angles of a quadrilateral is 180*2=360 degrees.

But knowing that one of the angles of a quadrilateral is 90 degrees does not mean that the other angles must also be 90 degrees. The sum of the remaining three angles must be 360-90=270 degrees. So, the remaining three angles can be 100, 100 and 70 or 100, 110, and 60, ...

Hope it's clear.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 08 Jan 2014
Posts: 20
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)
Followers: 1

Kudos [?]: 15 [0], given: 4

Re: Is quadrilateral ABCD a rectangle? [#permalink]

Show Tags

New post 10 May 2014, 12:00
Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
answer:"C"
Q2.
answer:"B"
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...
together it becomes a square..answer:"C"
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33499
Followers: 5928

Kudos [?]: 73443 [0], given: 9902

Re: Is quadrilateral ABCD a rectangle? [#permalink]

Show Tags

New post 11 May 2014, 06:04
Expert's post
ravishankar1788 wrote:
Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
answer:"C"
Q2.
answer:"B"
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...
together it becomes a square..answer:"C"


Please note that the OA is E, not C. Check here: is-quadrilateral-abcd-a-rectangle-100729.html#p778263

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Re: Is quadrilateral ABCD a rectangle?   [#permalink] 11 May 2014, 06:04
    Similar topics Author Replies Last post
Similar
Topics:
Is quadrilateral ABCD a rectangle? potatomaximum 0 12 Aug 2015, 04:07
2 Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? reto 7 06 Jun 2015, 04:24
2 Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? reto 1 06 Jun 2015, 04:17
4 Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? mattce 4 16 Jul 2013, 19:23
6 Experts publish their posts in the topic Is quadrilateral ABCD a rectangle? gottabwise 19 23 Jan 2010, 21:18
Display posts from previous: Sort by

Is quadrilateral ABCD a rectangle?

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


GMAT Club MBA Forum Home| About| 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®.