GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Aug 2019, 18:36

### 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

# Is quadrilateral MNPQ a rectangle?

Author Message
TAGS:

### Hide Tags

Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 102
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)

### Show Tags

03 Jul 2014, 04:45
1
2
00:00

Difficulty:

5% (low)

Question Stats:

79% (00:39) correct 21% (00:52) wrong based on 147 sessions

### HideShow timer Statistics

(1) At least two of the four angles are right angles.
(2) At least three of the four angles are right angles.
Math Expert
Joined: 02 Sep 2009
Posts: 57030

### Show Tags

03 Jul 2014, 05:09
1

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 57030

### Show Tags

03 Jul 2014, 05:10
Bunuel wrote:

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Similar questions to practice:

Hope it helps.
_________________
Intern
Joined: 22 Jun 2013
Posts: 35

### Show Tags

04 Jul 2014, 00:08
Bunuel wrote:

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?

Thankyou.
Math Expert
Joined: 02 Sep 2009
Posts: 57030

### Show Tags

04 Jul 2014, 02:48
niyantg wrote:
Bunuel wrote:

The sum of Interior Angles of a polygon is 180(n-2), where n is the number of sides. Hence the sum of the interior angles of quadrilateral is 180(4-2) = 360°.

(1) At least two of the four angles are right angles. The angles could be 90°, 90°, 90°, 90° (rectangle) or 90°, 90°, 100°, 80° (not a rectangle). Not sufficient.

(2) At least three of the four angles are right angles. The sum of these 3 angles is 3*90° = 270°, thus the measure of the fourth angle is 360° - 270° = 90°. Sufficient.

Hello Bunuel

I have a doubt here.
If all 4 angles are 90 degrees then it can be a square also.

We dont know whether all 4 sides or only 2 sides opposite sides are equal ?

So should B be the answer ?

Thankyou.

All squares are rectangles so if MNPQ is a square it's a rectangle too.
_________________
Intern
Joined: 21 Aug 2015
Posts: 22

### Show Tags

30 May 2017, 07:20
Bunuel What if all the four angles are 90 but opposite sides are not equal?
Math Expert
Joined: 02 Sep 2009
Posts: 57030

### Show Tags

30 May 2017, 07:52
Nitish7 wrote:
Bunuel What if all the four angles are 90 but opposite sides are not equal?

If all four angels are 90 degrees, then we have a rectangle, in rectangle all four angles are equal.
_________________
Intern
Joined: 23 Feb 2017
Posts: 36

### Show Tags

30 May 2017, 22:00
Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?
Retired Moderator
Joined: 22 Aug 2013
Posts: 1434
Location: India

### Show Tags

30 May 2017, 22:30
sasidharrs wrote:
Hi Banuel,
What if I have a square and tilt it clockwise by 45 degrees.. more like a rhombus..
its not rectangle right?

Hi

If you take a square and tilt it clockwise, it will still remain a square. When you say tilting, I assume you are just rotating that quadrilateral clockwise or anticlockwise.

A rhombus has all sides equal but all angles are not necessarily equal. So if all the angles are not equal to 90 degrees, then it will definitely not be a rectangle.
But it can surely be a rhombus.
As I wrote, a rhombus has all sides equal but all angles might not be equal, though opposite angles are always equal. A rhombus in which all angles are also equal - then becomes a square. So we say that all squares are rhombuses but all rhombuses are not squares.
Display posts from previous: Sort by