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

r = 100
Length of arc = 2(pi)(100)/4 = 50pi = ~150

Fencing needed = ~350. Ans C

Just C, from 2PR=circumference and multiplied by 1/4 + 200

Ans: C

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.

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.

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?

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.

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.

GMAT assassins aren't born, they're made,
Rich

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

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

(2*pi*100)/4 = 50*pi = 50*3 (estimating) 150 + 200 = 350, C fits.

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.

I never remember the formula for an Arc but here is how I calculated it

Information we know
1. This is 1/4 of a circle
2. The radius is 100

Hence we can solve for
1. The perimeter of the circle and divide by 4
>> we will get the length of the Arc
2. Add 100 + 100 because that is the inner length

Solve
> 100 + 100 [given info] + Arc

Arc = X
X = Pie*D or 2PieR
X = (3.14 * 200)/4
X = 3.15 * 50
X = 157


Hence

= 157 + 100 + 100
= 357

Ans: C

Circumference of the quarter of the circle= 2 π r/4= 2*22*100/4=157

Length of the fence=157+100+100=357.
C

In this question the 100ft looks like the diameter of the circle, how is that the radius of the fence?

100ft there shows radius. How is it the diameter???

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