Is quadrilateral ABCD a rectangle? : Data Sufficiency (DS)

My Profile Logout

Test's Subscription Expires:

My Follow Feed Kudos My Error Log

Messages and Replies

Settings Mark All Read

See All

Applicant Notifications

Settings Mark All Read

See All

Global notifications

Settings Mark All Read

See All

Is quadrilateral ABCD a rectangle?

Sort by Date

Sort by Kudos

Author

Message

TAGS:

Hide Tags

CEO

Joined: 11 Sep 2015

Posts: 3122

Location: Canada

Is quadrilateral ABCD a rectangle? [#permalink]

Show Tags

29 Nov 2016, 06:30

Top Contributor

00:00

Difficulty:

75% (hard)

Question Stats:

39% (01:06) correct

61% (01:03) wrong

based on 297 sessions

HideShow timer Statistics

Is quadrilateral ABCD a rectangle?

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

*Kudos for all correct solutions

Spoiler: OA

_________________

Test confidently with gmatprepnow.com

Math Expert

Joined: 02 Sep 2009

Posts: 50627

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

Show Tags

29 Nov 2016, 06:40

GMATPrepNow wrote:

Is quadrilateral ABCD a rectangle?

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

*Kudos for all correct solutions

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Senior CR Moderator

Status: Long way to go!

Joined: 10 Oct 2016

Posts: 1378

Location: Viet Nam

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

Show Tags

29 Nov 2016, 07:11

GMATPrepNow wrote:

Is quadrilateral ABCD a rectangle?

(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.

The answer is B.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Intern

Joined: 04 Mar 2016

Posts: 45

Location: India

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

Show Tags

29 Nov 2016, 07:23

nguyendinhtuong wrote:

GMATPrepNow wrote:

Is quadrilateral ABCD a rectangle?

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

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 !!

Senior CR Moderator

Status: Long way to go!

Joined: 10 Oct 2016

Posts: 1378

Location: Viet Nam

Is quadrilateral ABCD a rectangle? [#permalink]

Show Tags

29 Nov 2016, 07:30

Omkar.kamat wrote:

nguyendinhtuong wrote:

GMATPrepNow wrote:

Is quadrilateral ABCD a rectangle?

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

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: 45

Location: India

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

Show Tags

29 Nov 2016, 07:32

nguyendinhtuong wrote:

Omkar.kamat wrote:

nguyendinhtuong wrote:

[quote="GMATPrepNow"]Is quadrilateral ABCD a rectangle?

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

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 !!

Senior CR Moderator

Status: Long way to go!

Joined: 10 Oct 2016

Posts: 1378

Location: Viet Nam

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

Show Tags

29 Nov 2016, 07:44

Omkar.kamat wrote:

nguyendinhtuong wrote:

Is quadrilateral ABCD a rectangle?

(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.

The answer is B.

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 3369 times ]

_________________

Intern

Joined: 29 Jun 2016

Posts: 6

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

Show Tags

29 Nov 2016, 09:13

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.

so please tell me why not answer is C

CEO

Joined: 11 Sep 2015

Posts: 3122

Location: Canada

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

Show Tags

29 Nov 2016, 09:25

Top Contributor

vikrantsharma725@gmail.com wrote:

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:

_________________

Test confidently with gmatprepnow.com

Senior CR Moderator

Status: Long way to go!

Joined: 10 Oct 2016

Posts: 1378

Location: Viet Nam

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

Show Tags

29 Nov 2016, 17:42

vikrantsharma725@gmail.com wrote:

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: 6

GMAT 1: 640 Q48 V29

GMAT 2: 660 Q48 V34

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

Show Tags

20 Dec 2016, 04:34

Perfect nguyendinhtuong :D

Manager

Joined: 20 Feb 2017

Posts: 73

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

Show Tags

Updated on: 11 Sep 2017, 07:39

GMATPrepNow wrote:

vikrantsharma725@gmail.com wrote:

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, 17:40.
Last edited by goalMBA1990 on 11 Sep 2017, 07:39, edited 1 time in total.

Intern

Joined: 28 Nov 2014

Posts: 11

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

Show Tags

11 Sep 2017, 07:25

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

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

Show Tags

11 Dec 2017, 09:26

is-quadrilateral-rstv-a-rectangle-130928 .Please check it.

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.

CEO

Joined: 11 Sep 2015

Posts: 3122

Location: Canada

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

Show Tags

30 Apr 2018, 12:40

Top Contributor

goalMBA1990 wrote:

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?

(2) The sum of any 3 angles in the quadrilateral is 270 degrees
The key word here is ANY.
Let's call the 4 angles a, b, c and d
If ANY 3 angles add to 270, we can write 4 possible equations.
a + b + c = 270. This means that angle d MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
a + b + d = 270. This means that angle c MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
a + c + d = 270. This means that angle b MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
b + c + d = 270. This means that angle a MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
At this point, we shown that all 4 angles must equal 90 degrees.

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com