Last visit was: 15 Jul 2024, 14:09 It is currently 15 Jul 2024, 14:09
Toolkit
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?

SORT BY:
Tags:
Show Tags
Hide Tags
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30805 [41]
Given Kudos: 799
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30805 [9]
Given Kudos: 799
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6805
Own Kudos [?]: 30805 [7]
Given Kudos: 799
General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 94354
Own Kudos [?]: 641114 [4]
Given Kudos: 85011
1
Kudos
3
Bookmarks
Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1141
Own Kudos [?]: 6309 [2]
Given Kudos: 65
Location: Viet Nam
1
Kudos
1
Bookmarks
GMATPrepNow wrote:

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

Intern
Joined: 04 Mar 2016
Posts: 22
Own Kudos [?]: 15 [2]
Given Kudos: 2
Location: India
2
Kudos
nguyendinhtuong wrote:
GMATPrepNow wrote:

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1141
Own Kudos [?]: 6309 [1]
Given Kudos: 65
Location: Viet Nam
1
Kudos
Omkar.kamat wrote:
nguyendinhtuong wrote:
GMATPrepNow wrote:

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.

Sorry but the diagonals of a quadrilateral will never be parallel.

Rhombus is a quadrilateral that its diagonals are perpendicular, not parallel, at the midpoint of each.

Also, a Rhombus could be a square, so it is a rectangle, but a rectangle isn't necessarily a Rhombus

A Rectangle is a quadrilateral with 4 right angles
Intern
Joined: 04 Mar 2016
Posts: 22
Own Kudos [?]: 15 [0]
Given Kudos: 2
Location: India
nguyendinhtuong wrote:
Omkar.kamat wrote:
nguyendinhtuong wrote:

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.

Sorry but the diagonals of a quadrilateral will never be parallel.

Rhombus is a quadrilateral that its diagonals are perpendicular, not parallel, at the midpoint of each.

Also, a Rhombus could be a square, so it is a rectangle, but a rectangle isn't necessarily a Rhombus[/quote]
Sorry. I meant perpendicular.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1141
Own Kudos [?]: 6309 [4]
Given Kudos: 65
Location: Viet Nam
3
Kudos
1
Bookmarks
Omkar.kamat wrote:
Omkar.kamat wrote:
nguyendinhtuong wrote:

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.

Sorry. I meant perpendicular.

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

Here is why A is insufficient
Attachment:

Untitled.png [ 13.75 KiB | Viewed 10967 times ]
Intern
Joined: 29 Jun 2016
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 12
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1141
Own Kudos [?]: 6309 [3]
Given Kudos: 65
Location: Viet Nam
3
Kudos
vikrantsharma725@gmail.com wrote:
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

The answer is not C because we need only B enough to deduce that ABCD is a rectangle.

(1) is insufficient due to #7.

Let me make clearer in (1). If diagonals of ABCD are prependicular, ABCD could be a rhombus or not.
If ABCD is a rhombus, it could be a square or not.
If ABCD is a square, it's also a rectangle.

So (1) => ABCD could be a rectangle or not. Insufficient.

(2) A quadrilateral with 4 right angles is a rectangle. If ABCD is a square, it's clearly a rectangle since square is a special type of rectangle. In all cases, we have ABCD is a rectangle. So (2) is sufficient to answer the question.

Hope this helps.
Intern
Joined: 20 Sep 2016
Posts: 4
Own Kudos [?]: [0]
Given Kudos: 0
GMAT 1: 640 Q48 V29
GMAT 2: 660 Q48 V34
Perfect nguyendinhtuong :D
Intern
Joined: 21 Feb 2017
Posts: 49
Own Kudos [?]: 7 [1]
Given Kudos: 23
1
Bookmarks
GMATPrepNow wrote:
vikrantsharma725@gmail.com wrote:
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

Great question! In fact, it illustrates why I created the question in the first place.

A square is a type of rectangle. So, if the quadrilateral is a square, then we can also conclude that the quadrilateral is a rectangle.

From the Official Guide:
A parallelogram with right angles is a rectangle, and a rectangle with all sides of equal length is a square.

For more on this, here's a video:

I have a query for statement 2. We are told that sum of any 3 angles is 270. So how can we assume that each will be 90? It can be any value. So ans should be E. What am I missing?

Originally posted by goalMBA1990 on 03 Sep 2017, 18:40.
Last edited by goalMBA1990 on 11 Sep 2017, 08:39, edited 1 time in total.
Intern
Joined: 28 Nov 2014
Posts: 5
Own Kudos [?]: 2 [2]
Given Kudos: 112
2
Kudos
The sum of any 3 angles in the quadrilateral is 270 degrees.

It means the 4th angle will be 90 degree only. Try to understand it like this: If sum of angles a, b and c = 270 degree then angle d will be 90 degree. If sum of angles a, b and d = 270degree then angle c will be 90 degree and so on. So, it is a rectangle.
Intern
Joined: 14 Jul 2017
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 25

Sum of angles T, S, R is 270 degree and angle V is 90 degree. Yet TSRV is not a rectangle. So correct me why the answer should not be E.
Manager
Joined: 04 Jun 2017
Posts: 74
Own Kudos [?]: 38 [0]
Given Kudos: 180
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20
GPA: 3.82
B is correct

(1) is insufficient due to #7.

Let me make clearer in (1). If diagonals of ABCD are prependicular, ABCD could be a rhombus or not.
If ABCD is a rhombus, it could be a square or not.
If ABCD is a square, it's also a rectangle.

So (1) => ABCD could be a rectangle or not. Insufficient.

(2) A quadrilateral with 4 right angles is a rectangle. If ABCD is a square, it's clearly a rectangle since square is a special type of rectangle. In all cases, we have ABCD is a rectangle. So (2) is sufficient to answer the question.
Non-Human User
Joined: 09 Sep 2013
Posts: 33980
Own Kudos [?]: 851 [0]
Given Kudos: 0