NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 21:55 It is currently 24 Apr 2024, 21:55
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the area of a quadrilateral with a perimeter of 24 centimeters

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618844 [9]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   19 May 2015, 06:44
1
Kudos
8
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

45% (01:40) correct 55% (01:43) wrong based on 320 sessions
Hide Show timer Statistics
What is the area of a quadrilateral with a perimeter of 24 centimeters?

(1) The quadrilateral is formed by combining two isosceles right triangles
(2) All angles are of equal measure and the diagonals are perpendicular of each other.

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618844 [8]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   25 May 2015, 03:44
3
Kudos
4
Bookmarks
Expert Reply
Bunuel wrote:
What is the area of a quadrilateral with a perimeter of 24 centimeters?

(1) The quadrilateral is formed by combining two isosceles right triangles
(2) All angles are of equal measure and the width of the quadrilateral is 25% of the length


OFFICIAL SOLUTION:

What is the area of a quadrilateral with a perimeter of 24 centimeters?

(1) The quadrilateral is formed by combining two isosceles right triangles.

It's easy to fall into the trap and consider only the case when the two isosceles right triangles give a square (figure 1) but there are other cases possible, for example, when two isosceles right triangles give a parallelogram (figure 2):
Attachment:
Untitled.png
Untitled.png [ 1.98 KiB | Viewed 11051 times ]

So, this statement is not sufficient.

(2) All angles are of equal measure and the diagonals are perpendicular of each other.

The sum of interior angles of a quadrilateral is 360°. Thus, if all angles are of equal measure, then each angle must be 90°. So, we have a rectangle, with the diagonals which are perpendicular of each other. So, we have a square. Since the perimeter is 24, then 4x = 24. We can find x, hence we can find the area. Sufficient.

Answer: B.
General Discussion
User avatar
Jackal
Manager
Manager
Joined: 21 Feb 2012
Posts: 50
Own Kudos [?]: 118 [8]
Given Kudos: 63
Send PM
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 06:24
7
Kudos
1
Bookmarks
Quote:

According to me the answer should be D.

You can easily see from statement 1 that it is a square.

a + b + c + d= 24
4a =6
a=1.5

Area = 2.25 square centimeters

Where as the second statement yields a different value of the area.

Please check. I was saying it in that terms :-D



Hello. Good evening.

The statement 1 can be a square but always is not a square. Please refer attached diagram. As you rightly said this is not a well written problem. But in the Gmat world I think this is a smart problem.
Attachments

Untitledmmm.png
Untitledmmm.png [ 32.92 KiB | Viewed 7301 times ]

User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11172
Own Kudos [?]: 31895 [1]
Given Kudos: 290
Send PM
Reviews Badge
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   19 May 2015, 09:19
1
Kudos
Expert Reply
Bunuel wrote:
What is the area of a quadrilateral with a perimeter of 24 square centimeters?

(1) The quadrilateral is formed by combining two isosceles right triangles
(2) All angles are of equal measure and the width of the quadrilateral is 25% of the length




ans B..
statement one can help us form different quadrilateral having different proportions of sides. one where the two triangles meet are joined by their hyp and other where hyp of one is superimposed on the base/perp of the other.. so not sufficient
statement 2 tells us it is a rectangle and the ratio of sides is given.. sufficient
avatar
bluesquare
Intern
Intern
Joined: 29 Mar 2015
Posts: 39
Own Kudos [?]: 51 [1]
Given Kudos: 9
Location: United States
Send PM
GMAT ToolKit User Reviews Badge
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   19 May 2015, 18:27
1
Kudos
1: The quadrilateral can either be a square or a quadrilateral with sides X, X, X root 2, and 2X. In the first case, the perimeter is 4X -> X is 6, so area is 36, and in the second case, the perimeter is 4X + X root 2 -> the area is not 36. So 1 is not sufficient.

2: All angles are equal -> quadrilateral is a rectangle, and the width is 25% of the length, so the sides are X, X, .25X and .25X -> perimeter is 2.5X and so the area is calculate-able.

Therefore, 2 is sufficient, so the answer is B.
User avatar
Jackal
Manager
Manager
Joined: 21 Feb 2012
Posts: 50
Own Kudos [?]: 118 [1]
Given Kudos: 63
Send PM
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 05:37
1
Kudos
Quick approach

Statement 1: not possible as 24 needs to be divided into 2 pairs of equal numbers. Multiple possibilities. So out.

Statement 2: sufficient
concept - sum of interior angles of a convex quadrilateral is always 360 degrees (assuming we have only convex polygons in gmat)
Therefore quadrilateral is a rectangle. Its not a square as the relation between length and breadth is given. So solvable.
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1263 [1]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 06:29
1
Kudos
Jackal wrote:
Quote:

According to me the answer should be D.

You can easily see from statement 1 that it is a square.

a + b + c + d= 24
4a =6
a=1.5

Area = 2.25 square centimeters

Where as the second statement yields a different value of the area.

Please check. I was saying it in that terms :-D



Hello. Good evening.

The statement 1 can be a square but always is not a square. Please refer attached diagram. As you rightly said this is not a well written problem. But in the Gmat world I think this is a smart problem.


Oh Yes. Thanks a lot. :)

I tried forming the quadrilateral only by joining the two hypotenuses. But you are right in saying that it can be a square and cannot be a square. Well, you illustrated your point with a diagram that clears my doubt by joining the other triangle through the base of the first triangle.

Yes, this is a smart problem and well an add on to my error log.

Thank You Bunuel for the question :-D
User avatar
UJs
Manager
Manager
Joined: 18 Nov 2013
Posts: 68
Own Kudos [?]: 193 [1]
Given Kudos: 63
Concentration: General Management, Technology
Schools: Oxford'17 (WL) Insead July'17 (I) Judge'17 (D)
GMAT 1: 690 Q49 V34
Send PM
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 17:05
1
Kudos
What is the area of a quadrilateral with a perimeter of 24 square centimeters?

Stmt (1) : The quadrilateral is formed by combining two isosceles right triangles

if both the triangles have same sides say (1,1,2) & (1,1,2) then it can be a rectangle.
but if one triangle is (1,1,2) & (2, 2, 2\(\sqrt{2}\)) , then we can make one diagonal as 2 (2 as common side) and make a quadrilateral.

two different shapes Not sufficient

Stmt (2) : All angles are of equal measure and the width of the quadrilateral is 25% of the length
let angle of quadrilateral = a , then 4a = 360 , a = 90 (square or rectangle) , but length/width is mentioned so rectangle
now if length = x ; width = 25% of length = x/4

x + 0.25x = 24 ; can find length/width & area sufficient

Ans B
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1263 [0]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 05:50
Jackal wrote:
Quick approach

Statement 1: not possible as 24 needs to be divided into 2 pairs of equal numbers. Multiple possibilities. So out.

Statement 2: sufficient
concept - sum of interior angles of a convex quadrilateral is always 360 degrees (assuming we have only convex polygons in gmat)
Therefore quadrilateral is a rectangle. Its not a square as the relation between length and breadth is given. So solvable.


This question is badly written.

1. How can perimeter be in square centimeters ?
2. Answers are contradictory through both the statements! A rectangle and a square. How is that possible ?
User avatar
Jackal
Manager
Manager
Joined: 21 Feb 2012
Posts: 50
Own Kudos [?]: 118 [0]
Given Kudos: 63
Send PM
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 05:54
anewbeginning wrote:
Jackal wrote:
Quick approach

Statement 1: not possible as 24 needs to be divided into 2 pairs of equal numbers. Multiple possibilities. So out.

Statement 2: sufficient
concept - sum of interior angles of a convex quadrilateral is always 360 degrees (assuming we have only convex polygons in gmat)
Therefore quadrilateral is a rectangle. Its not a square as the relation between length and breadth is given. So solvable.


This question is badly written.

1. How can perimeter be in square centimeters ?
2. Answers are contradictory through both the statements! A rectangle and a square. How is that possible ?


totally agree on the framing of the question
1. Ignore square part in the units :)
2. But Square is a rectangle with all sides equal. please refer gmatclub math book.
User avatar
G
keats
Director
Director
Joined: 28 Nov 2014
Posts: 754
Own Kudos [?]: 1263 [0]
Given Kudos: 86
Concentration: Strategy
Schools: Fisher '19 (M$)
GPA: 3.71
Send PM
Reviews Badge
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   20 May 2015, 05:59
Jackal wrote:
anewbeginning wrote:
Jackal wrote:
Quick approach

Statement 1: not possible as 24 needs to be divided into 2 pairs of equal numbers. Multiple possibilities. So out.

Statement 2: sufficient
concept - sum of interior angles of a convex quadrilateral is always 360 degrees (assuming we have only convex polygons in gmat)
Therefore quadrilateral is a rectangle. Its not a square as the relation between length and breadth is given. So solvable.


This question is badly written.

1. How can perimeter be in square centimeters ?
2. Answers are contradictory through both the statements! A rectangle and a square. How is that possible ?


totally agree on the framing of the question
1. Ignore square part in the units :)
2. But Square is a rectangle with all sides equal. please refer gmatclub math book.


According to me the answer should be D.

You can easily see from statement 1 that it is a square.

a + b + c + d= 24
4a =6
a=1.5

Area = 2.25 square centimeters

Where as the second statement yields a different value of the area.

Please check. I was saying it in that terms :-D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32657
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink] New post   18 Sep 2022, 10:26
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.
GMAT Club Bot
gmatclubot
Re: What is the area of a quadrilateral with a perimeter of 24 centimeters [#permalink]
18 Sep 2022, 10:26
Moderator:
Bunuel
Math Expert
92900 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions