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D01-35

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D01-35  [#permalink]

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New post 16 Sep 2014, 00:13
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  75% (hard)

Question Stats:

47% (01:33) correct 53% (01:44) wrong based on 351 sessions

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Re D01-35  [#permalink]

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New post 16 Sep 2014, 00:13
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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
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Re: D01-35  [#permalink]

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New post 07 Jan 2015, 06:42
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..!
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Re: D01-35  [#permalink]

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New post 07 Jan 2015, 07:04
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.
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Re: D01-35  [#permalink]

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New post 07 Jan 2015, 09:22
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If I assume a rectangle with 11 X 14 then the perimeter would be 50. Where am I going wrong.
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Re: D01-35  [#permalink]

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New post 07 Jan 2015, 09:28
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Re D01-35  [#permalink]

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New post 24 May 2016, 21:07
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Why pai is 22/7?
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Re: D01-35  [#permalink]

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New post 25 May 2016, 08:49
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Re: D01-35  [#permalink]

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New post 25 Nov 2016, 07:24
This is like one of those tricky GMAT questions. I love it. Well done Bunuel
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Re D01-35  [#permalink]

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New post 28 Oct 2017, 03:15
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. The question even did not mention the shape !! how can you approach
GMAT CLUB should imediately correct the questions and make it state clearly that the shape is circle
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Re: D01-35  [#permalink]

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New post 28 Oct 2017, 03:18
zx33788115 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. The question even did not mention the shape !! how can you approach
GMAT CLUB should imediately correct the questions and make it state clearly that the shape is circle


The question is 100% correct.

The figure which has the minimum possible perimeter for a given area is a circle. This is a known mathematical property. 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.
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Re: D01-35  [#permalink]

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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.
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Re: D01-35  [#permalink]

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New post 07 Feb 2018, 01:52
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.
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Re: D01-35  [#permalink]

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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?
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Re: D01-35  [#permalink]

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New post 23 May 2018, 22:14
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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.
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Re: D01-35  [#permalink]

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New post 04 Jul 2018, 23:49
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Hi, is there an explanation as to why a circle is taken instead of a square?
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Re: D01-35  [#permalink]

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New post 05 Jul 2018, 00:00
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Re: D01-35  [#permalink]

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New post 26 Nov 2018, 11:09
I read this question 5 times before I realized it wanted a circle with an area of 154.

SOOOO tricky.
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Re: D01-35  [#permalink]

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New post 01 Feb 2019, 10:04
Bunuel wrote:
daraepark88 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Why pai is 22/7?


The question asks about the approximate length.

\(\pi = 3.1415...\) and 22/7 = 3.142..., and since we need only approximate value we can use 22/7 instead of \(\pi\) to simplify calculations.



One would need to remember that 22/7 is the approximate value of 3.14.. That's where I went wrong.
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Re D01-35  [#permalink]

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New post 26 Feb 2019, 19:35
I think this is a high-quality question and I agree with explanation.
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Re D01-35   [#permalink] 26 Feb 2019, 19:35

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