GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 23 Jan 2020, 21:56 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is quadrilateral ABCD a rectangle?

Author Message
TAGS:

### Hide Tags

Manager  Joined: 17 Nov 2009
Posts: 214

### Show Tags

1
6 00:00

Difficulty:   25% (medium)

Question Stats: 68% (00:48) correct 32% (00:59) wrong based on 278 sessions

### HideShow timer Statistics

(1) Angle ABC = 90 degrees
(2) AB = CD
Manager  Joined: 06 Jun 2009
Posts: 241
Location: USA
WE 1: Engineering

### Show Tags

agnok wrote:

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

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.
Manager  Joined: 20 Jul 2010
Posts: 172

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60627

### Show Tags

2
2
agnok wrote:

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

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 [ 4.39 KiB | Viewed 8511 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.
_________________
Manager  Joined: 17 Nov 2009
Posts: 214

### Show Tags

Manager  Joined: 20 Jul 2010
Posts: 172

### Show Tags

Thanks Bunuel for the diagram
Manager  B
Joined: 10 Mar 2014
Posts: 177

### Show Tags

Bunuel wrote:
agnok wrote:

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

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
Math Expert V
Joined: 02 Sep 2009
Posts: 60627

### Show Tags

PathFinder007 wrote:
Bunuel wrote:
agnok wrote:

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

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.
_________________
Intern  Joined: 08 Jan 2014
Posts: 16
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)

### Show Tags

Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
Q2.
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...
Math Expert V
Joined: 02 Sep 2009
Posts: 60627

### Show Tags

ravishankar1788 wrote:
Q1.
statement1>parallelogram
statement2>rectangle only if statement1 is true
Q2.
Q3
statement1>rectangle meaning all angles are 90
statement2> rhombus...

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

Hope it helps.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 14002

### Show Tags

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.
_________________ Display posts from previous: Sort by

# Is quadrilateral ABCD a rectangle?  