NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 15:42 It is currently 25 Apr 2024, 15:42
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

D01-35

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [106]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
D01-35 [#permalink] New post   16 Sep 2014, 00:13
11
Kudos
95
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

45% (01:30) correct 55% (01:40) wrong based on 899 sessions
Hide Show timer Statistics
What is the approximate minimum length of rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [40]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re D01-35 [#permalink] New post   16 Sep 2014, 00:13
12
Kudos
28
Bookmarks
Expert Reply
Official Solution:

What is the approximate minimum length of rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44


Since a circle has the smallest possible perimeter for a given area, enclosing a circular area would be the most efficient way to minimize the length of a rope.

Therefore, the 154 square meters should correspond to the area of a circle. To determine the length of the rope, we first need to calculate the radius of a circle with an area of 154 square meters, and then compute the circumference of the circle, which will be equal to the length of the rope. The formula for the area of a circle is \(area = \pi r^2 = 154\). We can approximate the radius by using an approximation for \(\pi\). A common approximation for \(\pi\) is \(\frac{22}{7}\). Thus, we have \(\frac{22}{7} * r^2 = 154\). This equation yields \(r^2 \approx 49\), and consequently, \(r \approx 7\).

The length of the rope will be equal to the circumference of the circle, which can be calculated as \(circumference = 2\pi r \approx 2*\frac{22}{7}*7 = 44\) meters.


Answer: E
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [14]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   23 May 2018, 22:14
8
Kudos
6
Bookmarks
Expert Reply
bondtradercu wrote:
Bunuel wrote:
sanjay1810 wrote:
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.


For triangles it's equilateral triangle but for any shape it's circle.



Hi - per MGMAT guide, it's the square that has the largest area? Could someone help reconcile?


1. For a triangle, the minimum possible perimeter for a given area is an equilateral triangle.
2. For a quadrilateral, the minimum possible perimeter for a given area is a square.
3. For any 2-D shape, so if there is no restriction on the shape, the minimum possible perimeter for a given area is a circle.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   05 Jul 2018, 00:00
2
Kudos
Expert Reply
kavyathach wrote:
Hi, is there an explanation as to why a circle is taken instead of a square?


Because a circle has the minimum possible perimeter for a given area. Foe example, if an area of a 2-D figure is say 10 unit^2, then the shape which has the minimum perimeter for that area is a circle. All other shapes with the area of 10 units^2 will have greater perimeter.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   28 Jul 2020, 11:29
2
Bookmarks
Expert Reply
AyeeshaJ wrote:
Hey Bunuel,

Thanks for this. Do these three shapes hold true the property that for a given perimeter, they have the highest area?

Look forward to your reply!

Bunuel wrote:
bondtradercu wrote:
Bunuel wrote:
sanjay1810 wrote:
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.


For triangles it's equilateral triangle but for any shape it's circle.



Hi - per MGMAT guide, it's the square that has the largest area? Could someone help reconcile?


1. For a triangle, the minimum possible perimeter for a given area is an equilateral triangle.
2. For a quadrilateral, the minimum possible perimeter for a given area is a square.
3. For any 2-D shape, so if there is no restriction on the shape, the minimum possible perimeter for a given area is a circle.


Generally, a regular polygon gives the maximum area for a given perimeter.

For example, a triangle with a given perimeter has a maximum area when it's regular, so when it's equilateral. A rectangle, when it's a square and so on.

For any 2-D shape, a circle has the maximum area for a given perimeter.
User avatar
vards
Manager
Manager
Joined: 25 Feb 2014
Status:PLAY HARD OR GO HOME
Posts: 109
Own Kudos [?]: 624 [1]
Given Kudos: 622
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
GPA: 3.1
Send PM
GMAT ToolKit User
Re: D01-35 [#permalink] New post   07 Jan 2015, 06:42
1
Bookmarks
Bunuel wrote:
Official Solution:

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44


Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: \(area=\pi r^2=154\). Now, the approximate value of \(\pi\) is \(\frac{22}{7}\), hence \(\frac{22}{7}*r^2=154\), which gives \(r^2 \approx 49\) and finally \(r \approx 7\).

The length of a rope will equal to the circumference of the circle: \(circumference=2\pi r \approx 2*\frac{22}{7}*7=44\).


Answer: E

Ohk..!Thanks Bunuel..!Could you please tell which shape be chosen when we are given the area and maximum length of the rope is to be found out ?
Thanks again..!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   07 Jan 2015, 07:04
1
Bookmarks
Expert Reply
vards wrote:
Bunuel wrote:
Official Solution:

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44


Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: \(area=\pi r^2=154\). Now, the approximate value of \(\pi\) is \(\frac{22}{7}\), hence \(\frac{22}{7}*r^2=154\), which gives \(r^2 \approx 49\) and finally \(r \approx 7\).

The length of a rope will equal to the circumference of the circle: \(circumference=2\pi r \approx 2*\frac{22}{7}*7=44\).


Answer: E

Ohk..!Thanks Bunuel..!Could you please tell which shape be chosen when we are given the area and maximum length of the rope is to be found out ?
Thanks again..!


You don';t need this for the GMAT, but anyway, for a given area, the perimeter is NOT limited.

For example, consider a rectangle with the area of 100. If the width approaches 0, then the length approaches infinity, which means that the perimeter is also approaches infinity.
avatar
B
skcmadduri
Intern
Intern
Joined: 29 Jul 2011
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 7
Concentration: Operations, Entrepreneurship
Schools: McCombs
GPA: 3.5
Send PM
GMAT ToolKit User
Re: D01-35 [#permalink] New post   07 Jan 2015, 09:22
1
Kudos
If I assume a rectangle with 11 X 14 then the perimeter would be 50. Where am I going wrong.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   07 Jan 2015, 09:28
1
Bookmarks
Expert Reply
skcmadduri wrote:
If I assume a rectangle with 11 X 14 then the perimeter would be 50. Where am I going wrong.


The question asks to find the approximate minimum possible length of a rope, which is 44: 44 < 50.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   07 Feb 2018, 01:52
1
Bookmarks
Expert Reply
sanjay1810 wrote:
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.


For triangles it's equilateral triangle but for any shape it's circle.
avatar
B
kavyathach
Intern
Intern
Joined: 22 Jan 2018
Posts: 6
Own Kudos [?]: 12 [1]
Given Kudos: 35
Send PM
Re: D01-35 [#permalink] New post   04 Jul 2018, 23:49
1
Kudos
Hi, is there an explanation as to why a circle is taken instead of a square?
avatar
B
sanjay1810
Intern
Intern
Joined: 19 Nov 2012
Posts: 8
Own Kudos [?]: 3 [0]
Given Kudos: 30
Send PM
Re: D01-35 [#permalink] New post   07 Feb 2018, 01:34
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.
avatar
B
eastcoastchamps
Manager
Manager
Joined: 28 Aug 2016
Posts: 161
Own Kudos [?]: 25 [0]
Given Kudos: 2
Send PM
Re: D01-35 [#permalink] New post   23 May 2018, 18:59
Bunuel wrote:
sanjay1810 wrote:
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.


For triangles it's equilateral triangle but for any shape it's circle.



Hi - per MGMAT guide, it's the square that has the largest area? Could someone help reconcile?
avatar
B
AyeeshaJ
Intern
Intern
Joined: 08 Aug 2019
Posts: 18
Own Kudos [?]: 39 [0]
Given Kudos: 136
GMAT 1: 700 Q50 V34
GPA: 3.5
Send PM
Reviews Badge
Re: D01-35 [#permalink] New post   28 Jul 2020, 10:39
Hey Bunuel,

Thanks for this. Do these three shapes hold true the property that for a given perimeter, they have the highest area?

Look forward to your reply!

Bunuel wrote:
bondtradercu wrote:
Bunuel wrote:
sanjay1810 wrote:
hello Bunuel

One quick question as there seems to be contradictory information:

For a given area, which figure has the less possible perimeter?
As per the question above, it's circle.
However, as per your own post on all information on triangles, it's equilateral triangle.
I cant add the link to your own post here as I'm a new member and there seems to be some restriction with posting links.

Please explain. If both are applicable in different scenarios, then do share these scenarios.

Thanks.


For triangles it's equilateral triangle but for any shape it's circle.



Hi - per MGMAT guide, it's the square that has the largest area? Could someone help reconcile?


1. For a triangle, the minimum possible perimeter for a given area is an equilateral triangle.
2. For a quadrilateral, the minimum possible perimeter for a given area is a square.
3. For any 2-D shape, so if there is no restriction on the shape, the minimum possible perimeter for a given area is a circle.
User avatar
L
AnirudhaS
LBS Moderator
Joined: 30 Oct 2019
Posts: 836
Own Kudos [?]: 775 [0]
Given Kudos: 1577
Send PM
Re: D01-35 [#permalink] New post   02 Jul 2022, 04:06
I think this is a high-quality question.
User avatar
B
Navz
Intern
Intern
Joined: 04 Mar 2020
Posts: 9
Own Kudos [?]: 12 [0]
Given Kudos: 29
Send PM
Re: D01-35 [#permalink] New post   26 Jul 2022, 13:30
My 2 cents:

More the symmetry of the shape, lower the perimeter for any given area.
In simple words , for a polygon, as the number of edges increases, the symmetry increases.
Circle can be thought of as a shape with infinite number of edges. If we keep increasing the number of edges in a regular polygon we will eventually get a circle.
Triangle ->Square-> pentagon-> hexagon-> heptagon-> octagon->nonagon-> decagon->.................-> Circle

PS: rectangle (2 axes of symmetry) is more symmetric than any triangle (1 axes of symmetry), except equilateral triangle (3 axes of symmetry)
User avatar
B
theGisforGorilla
Intern
Intern
Joined: 02 Feb 2023
Posts: 40
Own Kudos [?]: 22 [0]
Given Kudos: 47
GMAT 1: 780 Q49 V49
Send PM
Re: D01-35 [#permalink] New post   04 Mar 2023, 11:20
I think this is a high-quality question and I agree with explanation. Excellent question. I fell into the trap of looking for a square.


Off-topic question:
If you start looking for a rectangle with sides a,b; you get the following:

{ab=154
{2(a+b)=min

{b=154/a
{a+b=min

a+154/a = min
(a^2+154)/a = min

What is the formal way for a mathematician to solve (a^2+154)/a = min ?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619020 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   09 May 2023, 01:26
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
P
BottomJee
DI Forum Moderator
Joined: 05 May 2019
Status:GMAT Club Team member
Affiliations: GMAT Club
Posts: 1031
Own Kudos [?]: 638 [0]
Given Kudos: 1003
Location: India
GMAT Focus 1:
645 Q82 V81 DI82
GMAT 1: 430 Q31 V19
GMAT 2: 570 Q44 V25
GMAT 3: 660 Q48 V33
GPA: 3.26
WE:Engineering (Manufacturing)
Send PM
Reviews Badge CAT Tests Forum Quiz Mode
Re: D01-35 [#permalink] New post   12 Aug 2023, 09:53
I think this is a high-quality question and I agree with explanation.
GMAT Club Bot
gmatclubot
Re: D01-35 [#permalink]
12 Aug 2023, 09:53
Moderator:
Bunuel
Math Expert
92915 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