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Circle P shown above is centered at P. If the length of arc ABC is 40,

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Joined: 02 Sep 2009
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Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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06 Feb 2020, 07:16
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35% (medium)

Question Stats:

76% (01:28) correct 24% (02:18) wrong based on 49 sessions

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Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?

A. $$\frac{10,000}{\pi^{2}}$$

B. $$\frac{10,000}{\pi}$$

C. 10,000

D. $$10000\pi$$

E. $$10,000\pi^{2}$$

Attachment:

T6140.png [ 6.29 KiB | Viewed 586 times ]

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Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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06 Feb 2020, 07:42
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Bunuel wrote:

Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?

A. $$\frac{10,000}{\pi^{2}}$$

B. $$\frac{10,000}{\pi}$$

C. 10,000

D. $$10000\pi$$

E. $$10,000\pi^{2}$$
Attachment:
T6140.png

Since the answer choices are very spread apart, we can use estimation to quickly arrived at the correct answer.

Useful property: On the GMAT, the geometric diagrams in Problem Solving questions are assumed to be drawn to scale unless stated otherwise.

If arc ABC = 40, then the radius is approximately 30 (eyeballing)

Area of a circle $$= {\pi}r^2$$
$$≈ {\pi}(30^2)$$
$$≈ (3.1)(900)$$
$$≈ 3000$$

When we check the answer choices, answer choice B is the only answer choice that is remotely close to 3000

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Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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06 Feb 2020, 09:30
72/360 * 2*pi* r = 40
find r = 100/pi
area = $$\frac{10,000}{\pi}$$
IMO B

Bunuel wrote:

Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?

A. $$\frac{10,000}{\pi^{2}}$$

B. $$\frac{10,000}{\pi}$$

C. 10,000

D. $$10000\pi$$

E. $$10,000\pi^{2}$$

Attachment:
T6140.png
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9984
Location: United States (CA)
Re: Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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08 Feb 2020, 12:28
1
Bunuel wrote:

Circle P shown above is centered at P. If the length of arc ABC is 40, what is the area of circle P?

A. $$\frac{10,000}{\pi^{2}}$$

B. $$\frac{10,000}{\pi}$$

C. 10,000

D. $$10000\pi$$

E. $$10,000\pi^{2}$$

Attachment:
T6140.png

We can determine the circumference of the circle using the proportion:

72/360 = 40/C

1/5 = 40/C

C = 200

Therefore, the circumference of the circle is 200. We can determine the radius of the circle using the equation:

2πr = 200

πr = 100

r = 100/π

Thus, the area of the circle is:

π(100/π)^2 = 10,000π/π^2 = 10,000/π

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Circle P shown above is centered at P. If the length of arc ABC is 40,  [#permalink]

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09 Feb 2020, 03:05
Formula of Length of Arc = 2πr C/360 , where C = central angel
We are given, Length of Arc = 40
Central angel, C = 72
As per question, 2πr C/360 = 40
2πr 72/360 = 40
r = 100/π

Area, πr^2 = π(100/π)^2 = 10000/π
Circle P shown above is centered at P. If the length of arc ABC is 40,   [#permalink] 09 Feb 2020, 03:05
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