Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 888
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
06 Jun 2015, 03:24
1
This post received KUDOS
6
This post was BOOKMARKED
Question Stats:
49% (00:29) correct 51% (00:32) wrong based on 259 sessions
HideShow timer Statistics
Is quadrilateral ABCD a rectangle? (1) All four sides of ABCD are equal. (2) All four internal angles of ABCD are equal. SOLUTION: The issue is finding whether ABCD is a rectangle. A rectangle is a quadrilateral with parallel sides and four right angles.
According to Stat. (1) ABCD can be a square, which a subcategory of rectangle, yielding an answer of "yes". However, ABCD can also be a rhombus, which does not have right angles, and then then answer is "no". No definite answer, so Stat.(1)>maybe>IS>BCE.
Stat. (2): the sum of the angles in a quadrilateral is 360 degrees. If all angles are equal, each of them measure 360 / 4 = 90°. Therefore, ABCD is a rectangle (it can also be a square, which is a subcategory of a rectangle), and the answer is a definite "yes". Stat.(2)>'yes'>S>B.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.
Last edited by Bunuel on 06 Jun 2015, 09:50, edited 1 time in total.
Renamed the topic and edited the question.



Veritas Prep GMAT Instructor
Joined: 23 Oct 2013
Posts: 144

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
06 Jun 2015, 13:04
1
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well. Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.Answer choice B. I hope this helps!
_________________
Brandon Veritas Prep  GMAT Instructor
If you found this post helpful, please give me kudos!!!
Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews



Senior Manager
Joined: 27 Jul 2014
Posts: 321
GPA: 3.76

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 11:27
VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! Hi Brandon, Just a small doubt here. As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90. But this can be true for square also , so how can we determine its rectangle. It can be square also. Kindly let me know what I am missing here



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 11:32
kanigmat011 wrote:
Hi Brandon,
Just a small doubt here. As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90. But this can be true for square also , so how can we determine its rectangle. It can be square also.
Kindly let me know what I am missing here Rectangle is the BIGGER category while square is a special type of rectangle that has all angles equal to 90, all sides equal and diagonals being perpendicular bisectors of each other. Thus any square will always be a rectangle but the vice versa may or may not be true (as for a square you also need to have all angles = 90).



Retired Moderator
Joined: 06 Jul 2014
Posts: 1269
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 11:32
kanigmat011 wrote: VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! Hi Brandon, Just a small doubt here. As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90. But this can be true for square also , so how can we determine its rectangle. It can be square also. Kindly let me know what I am missing here Hello kanigmat011Square is a type of rectangle. So square is always a rectangle but rectangle is not always a square
_________________
Simple way to always control time during the quant part. How to solve main idea questions without full understanding of RC. 660 (Q48, V33)  unpleasant surprise 740 (Q50, V40, IR3)  antidebrief



Senior Manager
Joined: 27 Jul 2014
Posts: 321
GPA: 3.76

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 12:18
Harley1980 wrote: kanigmat011 wrote: VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! Hi Brandon, Just a small doubt here. As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90. But this can be true for square also , so how can we determine its rectangle. It can be square also. Kindly let me know what I am missing here Hello kanigmat011Square is a type of rectangle. So square is always a rectangle but rectangle is not always a square Thanks Harvey It just never popped my head.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1269
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 12:23
1
This post was BOOKMARKED



Senior Manager
Joined: 27 Jul 2014
Posts: 321
GPA: 3.76

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
04 Aug 2015, 12:34
Engr2012 wrote: kanigmat011 wrote:
Hi Brandon,
Just a small doubt here. As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90. But this can be true for square also , so how can we determine its rectangle. It can be square also.
Kindly let me know what I am missing here Rectangle is the BIGGER category while square is a special type of rectangle that has all angles equal to 90, all sides equal and diagonals being perpendicular bisectors of each other. Thus any square will always be a rectangle but the vice versa may or may not be true (as for a square you also need to have all angles = 90). Thanks Engr2012 Now its clear!



Manager
Joined: 20 Feb 2017
Posts: 86

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
08 May 2017, 05:25
VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! One doubt: Is it true that in DS and PS question, we have to consider every Square as a rectangle by default? Sent from my XT1663 using GMAT Club Forum mobile app



Math Expert
Joined: 02 Sep 2009
Posts: 43896

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
08 May 2017, 07:53
goalMBA1990 wrote: VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! One doubt: Is it true that in DS and PS question, we have to consider every Square as a rectangle by default? Sent from my XT1663 using GMAT Club Forum mobile appYes, but it has nothing to do with DS or PS specifically. Mathematically every square is a rectangle.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Mar 2017
Posts: 4
Location: India
WE: General Management (Energy and Utilities)

Re: Is quadrilateral ABCD a rectangle? [#permalink]
Show Tags
12 Jan 2018, 00:27
kanigmat011 wrote: VeritasPrepBrandon wrote: It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.
Is quadrilateral ABCD a rectangle? A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.
(1) All four sides of ABCD are equal. This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.
(2) All four internal angles of ABCD are equal. Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle > (32)*180 = 180. quadrilateral > (42)*180 = 360. pentagon > (52)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.
Answer choice B. I hope this helps! Hi Brandon, I'm still confused . Even if we know all angles are equal & 90 degree that gives us , no information about sides being equal to each other. Unless we combine both statement 1 & 2 .The option should have been C. Please help in explaining how ans choice B alone is sufficient. Thanks in advance.




Re: Is quadrilateral ABCD a rectangle?
[#permalink]
12 Jan 2018, 00:27






