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Math Expert V
Joined: 02 Sep 2009
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4
32 00:00

Difficulty:   75% (hard)

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

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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15
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: $$circumference=2\pi r \approx 2*\frac{22}{7}*7=44$$.

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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: $$circumference=2\pi r \approx 2*\frac{22}{7}*7=44$$.

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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Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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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: $$circumference=2\pi r \approx 2*\frac{22}{7}*7=44$$.

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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If I assume a rectangle with 11 X 14 then the perimeter would be 50. Where am I going wrong.
Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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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.
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Why pai is 22/7?
Math Expert V
Joined: 02 Sep 2009
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daraepark88 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Why pai is 22/7?

$$\pi = 3.1415...$$ and 22/7 = 3.142..., and since we need only approximate value we can use 22/7 instead of $$\pi$$ to simplify calculations.
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This is like one of those tricky GMAT questions. I love it. Well done Bunuel
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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
Math Expert V
Joined: 02 Sep 2009
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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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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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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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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 59632

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1
1
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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Hi, is there an explanation as to why a circle is taken instead of a square?
Math Expert V
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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.
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I read this question 5 times before I realized it wanted a circle with an area of 154.

SOOOO tricky.
Intern  Joined: 22 Jun 2012
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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?

$$\pi = 3.1415...$$ 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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I think this is a high-quality question and I agree with explanation. Re D01-35   [#permalink] 26 Feb 2019, 19:35

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# D01-35

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