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# What is the area of the region AOB shaded shown as above?

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Math Revolution GMAT Instructor
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What is the area of the region AOB shaded shown as above?  [#permalink]

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Updated on: 08 Jun 2018, 08:19
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66% (01:17) correct 34% (01:27) wrong based on 124 sessions

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There is a circle with the center O as above. What is the area of the sector AOB?

1) $$∠AOB=120^o$$
2) $$AB=50$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 08 May 2017, 03:04. Last edited by MathRevolution on 08 Jun 2018, 08:19, edited 1 time in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6369 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the area of the region AOB shaded shown as above? [#permalink] ### Show Tags 10 May 2017, 01:28 ==> In the original condition, you need to find the radius of the circle and the central angle, so there are 2 variable. In order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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10 May 2017, 10:13
Can you let me know how did you solve this question.
How you come to know O is center of the circle.
I thought answer is E
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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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10 May 2017, 10:30
1
1. Angle is 120°, however we would need the radius and something to find the area of triangle. So this statement is insufficient.
2. Length of the chord is given here, however this statement alone is insufficient.

Combining both we would get the radius and subsequently the area of triangle.

So answer should be C

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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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20 May 2017, 02:46
My take is E
It has to be explicitly mentioned that O is the center of the circle !!!!!!
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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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07 May 2018, 15:33
MathRevolution wrote:
Attachment:
5.8.png

What is the area of the region AOB shaded shown as above?

1) $$∠AOB=120^o$$
2) $$AB=50$$

Solution
Statement 1: not sufficient, as we can not find anything from this.
Statement 2: AB= 50 can not help us to find anything
Statement 1+2: radius of the circle can be found using formula lengh(AB)=2(pi)r*angle/360. As triangle ABC forms isosceles triangle.... its height can be found out, and hence Area of ABC can be determined.
Ans is C
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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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Updated on: 07 May 2018, 20:17
Since it can not be inferred from the question stem / statements that O is the centre of the circle. We can't take O as the centre.
Hence circle has no role to play.

Now the question reduces to a triangle OAB, where angle AOB is 120 deg and side AB = 50.
Now can we find the area of triangle? NO.

We can have different triangles of different areas satisfying given conditions.

Answer shall be E.

See the image:
Attachment:

SnipImage.JPG [ 15.22 KiB | Viewed 508 times ]

Angle O is 120deg, side AB = Side A'B' but areas are different.

(PS: Dont worry about circle, we can always draw many circles passing through 2 given points.)
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Originally posted by gmatbusters on 07 May 2018, 19:06.
Last edited by gmatbusters on 07 May 2018, 20:17, edited 1 time in total.
Image added for clarity
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Re: What is the area of the region AOB shaded shown as above?  [#permalink]

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11 May 2018, 05:57
MathRevolution

Recheck the Question OA

gmatbusters wrote:
Since it can not be inferred from the question stem / statements that O is the centre of the circle. We can't take O as the centre.
Hence circle has no role to play.

Now the question reduces to a triangle OAB, where angle AOB is 120 deg and side AB = 50.
Now can we find the area of triangle? NO.

We can have different triangles of different areas satisfying given conditions.

Answer shall be E.

See the image:
Attachment:
SnipImage.JPG

Angle O is 120deg, side AB = Side A'B' but areas are different.

(PS: Dont worry about circle, we can always draw many circles passing through 2 given points.)

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Re: What is the area of the region AOB shaded shown as above? &nbs [#permalink] 11 May 2018, 05:57
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# What is the area of the region AOB shaded shown as above?

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