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# GMAT Diagnostic Test Question 36

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GMAT Diagnostic Test Question 36 [#permalink]

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06 Jun 2009, 23:23
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GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750

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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Last edited by bb on 29 Sep 2013, 21:41, edited 2 times in total.
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Re: GMAT Diagnostic Test Question 36 [#permalink]

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10 Jun 2009, 20:10
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Explanation

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: $$area=\pi{r^2}=154$$ --> approximate value of $$\pi$$ is $$\frac{22}{7}$$ --> $$\frac{22}{7}*{r^2}=154$$ --> $$r^2\approx{49}$$ --> $$r\approx{7}$$.

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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Last edited by bb on 28 Sep 2013, 21:46, edited 1 time in total.
Updated
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Re: GMAT Diagnostic Test Question 36 [#permalink]

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01 Oct 2012, 08:20
bb wrote:
GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750
 Rating:

If an $$x$$ meter long rope can enclose (or cover) a maximum area of 50 square meters, what is the approximate length of the rope?

A. 4
B. 7
C. 10
D. 20
E. 25

BELOW IS REVISED VERSION OF THIS QUESTION:

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: $$area=\pi{r^2}=154$$ --> approximate value of $$\pi$$ is $$\frac{22}{7}$$ --> $$\frac{22}{7}*{r^2}=154$$ --> $$r^2\approx{49}$$ --> $$r\approx{7}$$.

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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Re: GMAT Diagnostic Test Question 36 [#permalink]

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16 Dec 2013, 02:14
bb wrote:
GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750

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

Dear bb,

I understand that Im just a beginner but this question well bellow 600 cause even I solved it in seconds.
just a friendly suggestion
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Re: GMAT Diagnostic Test Question 36 [#permalink]

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18 Dec 2013, 07:09
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Math Expert
Joined: 02 Sep 2009
Posts: 38910
Followers: 7741

Kudos [?]: 106305 [0], given: 11620

Re: GMAT Diagnostic Test Question 36 [#permalink]

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18 Dec 2013, 07:13
aakrity wrote:
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Hope it helps.
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Joined: 08 Oct 2011
Posts: 42
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Re: GMAT Diagnostic Test Question 36 [#permalink]

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18 Dec 2013, 07:19
Bunuel wrote:
aakrity wrote:
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Hope it helps.

Yes, the post helps. Thank you.
Re: GMAT Diagnostic Test Question 36   [#permalink] 18 Dec 2013, 07:19
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# GMAT Diagnostic Test Question 36

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