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# The figure shown represents a piece of land that is in the

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Manager
Joined: 28 Aug 2006
Posts: 121
The figure shown represents a piece of land that is in the  [#permalink]

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Updated on: 24 Jul 2013, 08:15
3
29
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:25) correct 24% (01:35) wrong based on 418 sessions

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fence.gif [ 2.44 KiB | Viewed 36708 times ]
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441

Originally posted by humtum0 on 02 Sep 2007, 19:52.
Last edited by Bunuel on 24 Jul 2013, 08:15, edited 2 times in total.
Edited the question and moved to PS forum.
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SVP
Joined: 06 Nov 2014
Posts: 1877
Re: The figure shown represents a piece of land that is in the  [#permalink]

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12 Jun 2016, 22:27
6
3
Length of the fence means the perimeter of the fence.

Perimeter = 100 + 100 + length of the arc
Length of the arc = 2*π*100 / 4 {Quarter of a circle} = 50π = 157

Perimeter = 100 + 100 + 157 = 357

Correct Option: C
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Director
Joined: 30 Jun 2007
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03 Sep 2007, 00:56
10
2
Answer C:

The Central Angle of the Circle is 90.
The length of the Arc = (90/360) * Circumference of the Circle
= 2* pi * 100 / 4 = 2 * pi * 25 = 50 * 3.14 = 157

Perimeter of the Arc = 100 + 100 + 157 = 357
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02 Sep 2007, 20:16
2
1
r = 100
Length of arc = 2(pi)(100)/4 = 50pi = ~150

Fencing needed = ~350. Ans C
Manager
Joined: 27 Aug 2007
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04 Sep 2007, 22:49
1
Just C, from 2PR=circumference and multiplied by 1/4 + 200

Ans: C
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Re: GMATPrep Question -- Land enclosed by fence?  [#permalink]

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04 Sep 2007, 23:11
Length = [(2.pi.r)/4+2r] = r(pi+4)/2=r(3.14+4)/2=r x 3.57
When r is 100, length will be 357

Regards.

humtum0 wrote:
The figure represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence , which of the following is the closest to the length , in feet, of the fence?

A. 278
B. 341
C. 357
D. 400
E. 441

OA ----> C

Please explain.
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Re: GMATPrep Question -- Land enclosed by fence?  [#permalink]

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06 Sep 2007, 21:14
3
2
humtum0 wrote:
The figure represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence , which of the following is the closest to the length , in feet, of the fence?

A. 278
B. 341
C. 357
D. 400
E. 441

OA ----> C

Please explain.

Wish I got this on my gmatprep. If u know the rules of circles and what not, this is a gimme problem.

Essentially the question is asking us for the perimeter of the quarter circle.

P= Side1+side2+arc length of the 1/4 circle. radius is 100ft so the diameter is 200ft.

Circum=200pi.

to find the arc length take the degrees of the center of the circle given here as 90degrees and divide it by the total degrees of the circle. So 90/360=1/4.

1/4*200pi=50pi

P=100+100+50pi ---> 200+50pi. U must know that pi is rougly 3.14 or even just 3. so 200+150=350. Closest answer to this is C.
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Re: The figure represents a piece of land that is in the shape  [#permalink]

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24 Jul 2013, 06:55
2
The way I did this one was the maximum value if we draw a square would be 400

and if we use Pythagorean theorem we get 100 + 100 + 100 $$\sqrt{2}$$

The value will be greater than this and less than 400 so answer is 357

any other alternative methods to solve this question?
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Posts: 41
The figure shown represents a piece of land that is in the  [#permalink]

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09 Jul 2015, 04:01
humtum0 wrote:
Attachment:
fence.gif
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441

OBSERVATION on this Question

i couldn't understand this problem, i saw this problem while i was doing gmat prep 2, i was kind of doing bad in prep test, and the moment i saw this problem, i thought fencing hummm..that seems an easy one--i have to add 100 + 100 + 1/4 of the circumference.

so i quickly applied this formula 2pie r == 2pie100 =200 pie, so i knew i needed one forth of it, so 1/4*200= 50, so far i was kinda going good, but then 100+100+50 = 250 ( and i tried to read the question again but it didn't help, i tried checking my calculation but wasted my time,i didn't want to skip this question cause i knew it was a low difficulty problem, so on actual GMAT the penalty would have been higher, because of that i was little stubborn (though i shouldn't have been),but i was feeling anxious and frustrated at the same time so i ended the test realizing that i had fallen prey to a trap of GMAT test makers,
And now in introspect i see how close i was solving this problem all i had to do was to multiply 50*pie(3.14)= 157 + 200=370 answer C.

But i confess, GMAT was able to throw me off balance by an easy problem, and i got panicked, hope so i won't do it in the real test.
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Re: The figure shown represents a piece of land that is in the  [#permalink]

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09 Jul 2015, 20:48
4
Hi jaspreets,

You've properly identified the mistake that you made, which is a good bit of self-analysis. Now that you KNOW the mistake, what would you have done differently the first time you tackled this question? I'll bet that you did not write enough on your pad (Did you write down the formula for circumference? Did you write down the pi symbol? Did you write down the numbers? Did you do ANYTHING in your head?). The truth is that the silliest mistakes cost most Test Takers dearly....so you have to do MORE work on the pad to keep those little mistakes from happening. The good news is that the work is actually pretty easy AND it doesn't take too much extra time or effort; now you just have to make that extra note-taking process a part of how you tackle ALL questions.

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Re: The figure shown represents a piece of land that is in the  [#permalink]

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01 Aug 2017, 17:08
2
humtum0 wrote:
Attachment:
fence.gif
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441

We must determine how much fence is needed to enclose the quarter circle.

The curvy part of the fence, which is called an arc, has a length that is equal to ¼ of the circumference of the entire circle.

Since the circle's radius = 100 feet, we can use the following equation:

Circumference = 2πr

Circumference = 2 x π x 100 = 200π

Thus, ¼ of the circumference = ¼ x 200π = 50π

50π ≈ 50 x 3.14 = 157

To enclose the entire quarter circle, we would need approximately 100 + 100 + 157 = 357 feet of fence.

Answer: C
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Re: The figure shown represents a piece of land that is in the  [#permalink]

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19 Jan 2019, 09:21
humtum0 wrote:
Attachment:
fence.gif
The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278
(B) 341
(C) 357
(D) 400
(E) 441

We are looking for 1/4th the circumference + 200

(2*pi*100)/4 = 50*pi = 50*3 (estimating) 150 + 200 = 350, C fits.
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Re: The figure shown represents a piece of land that is in the  [#permalink]

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01 Apr 2019, 02:51
Had a brain-fart moment and didn't notice that the 100ft was equal to the radius of the quarter circle.

So what I did was I thought "what if the fence was triangular?" If that was the case the length of the 3rd side of the triangle would be in the ratio of $$1:1:\sqrt{2}$$, meaning the total fence needed would be $$1 + 1 + \sqrt{2} ~= 3.14$$, or in our case around 314m.

BUT, it is NOT a triangle but a quarter circle so the distance of that side must be slightly longer, hence C and 357.

Not a great solution, but thought it was worthwhile pointing out how many different ways there are to reach the same conclusion.
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Re: The figure shown represents a piece of land that is in the   [#permalink] 01 Apr 2019, 02:51
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