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# D01-35

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:13
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65% (hard)

Question Stats:

58% (00:56) correct 42% (01:00) wrong based on 273 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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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: $$circumference=2\pi r \approx 2*\frac{22}{7}*7=44$$.

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

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

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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07 Jan 2015, 09:22
If I assume a rectangle with 11 X 14 then the perimeter would be 50. Where am I going wrong.
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07 Jan 2015, 09:28
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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19 Mar 2015, 02:34
I think this question is good and helpful.
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27 Jul 2015, 17:09
Hi Bunuel,
Why a circle has the minium possible perimeter for a given area?
Tks!
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30 Nov 2015, 10:44
Hi Bunuel

I just wanted to clarify is it square or circle which has the minimum perimeter for the given area
As per one of the GMAT guides = "Of all quadrilaterals with a given area, the square has the minimum perimeter."

Thanks
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18 Dec 2015, 13:34
I guess the question should have mentioned a "circular" area. Because nothing is telling us that we are supposed to find a circumference instead of a perimeter. I went with a rectangular of 11 14 too.
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18 Dec 2015, 13:35
Bunuel 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.

I spoke too fast. Then this is a hard question.
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18 Dec 2015, 13:41
sigma wrote:
Hi Bunuel

I just wanted to clarify is it square or circle which has the minimum perimeter for the given area
As per one of the GMAT guides = "Of all quadrilaterals with a given area, the square has the minimum perimeter."

Thanks

I don't think you can compare a circle to a quadri since you don't use the same input to compute them. Your statement is true but only applies to quadris. The trick here was that we weren't given the shape de la landbank and that the quadri was easy to spot.
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17 Feb 2016, 12:54
I fell for the "square meters" trap as well. I assumed that meant that the shape had to be a square.

After knowing that it could be a circle, I rounded pi down to 3 and the area up to 156 and got r is close to 7.

Circumference = 2*3*7 = closest to 44.
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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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25 May 2016, 08:49
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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18 Jun 2016, 14:53
It is the first time I face a question like that.

Is that given that when no shape is described, then we must figure out it?

Thanks and sorry for my dumb question
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05 Jul 2016, 10:04
Bunuel wrote:
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

Hi Bunuel,

Can you please explain how to figure out in the above question- the area given is the area of circle but not square!

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07 Aug 2016, 02:45
I think this is a high-quality question and I agree with explanation.
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28 Aug 2016, 02:14
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hello,

Sorry, I am not clear as to how to determine this question is referring to the area of a 'circle'?
I am not clear with what question is in fact asking.
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28 Aug 2016, 02:15
Hello,

How can I tell that question refers to 'circle' area?
Re D01-35 &nbs [#permalink] 28 Aug 2016, 02:15

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# D01-35

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