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What is the area of the circular region with center O?

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What is the area of the circular region with center O?

by BTGmoderatorLU » Sat Jun 16, 2018 2:28 pm

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In the figure above, what is the area of the circular region with center O?

1) MN is perpendicular to RS.
2) The area of triangular region OMT is 4.

The OA is E.

Please, can anyone explain why E is the correct answer? I'm confused. Thanks!
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Source: — Data Sufficiency |
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by arosman » Wed Jun 20, 2018 2:11 pm

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Since area = pi * r^2 we can rephrase this question as: What is the radius OM = OR = OS = ON?

1) MN is perpendicular to RS.
- This tells us MOT is a right triangle but without more info isn't going to help us find the radius
-----> INSUFFICIENT



2) The area of triangular region OMT is 4.
- Doesn't help cuz we don't know if MO is a height or OT is a base
------> INSUFFICIENT

1 & 2) Now we know MOT is a right triangle with area 4.
- area triangle = .5 * b * h
- area MOT = 4 = .5 * MO * OT
- This is about as far as we can get. We can't solve for MO.
- We can also use examples to show that we can get an area of 4 with multiple values for MO

Example 1:
MO = 8
OT = 1
area MOT = .5 * 8* 1 = 4

Example 2:
MO = 4
OT = 2
area MOT = .5 * 4 * 2 = 4

Multiple radii = multiple areas for circle ----> INSUFFICIENT

Answer: E

Can you show how you got a different answer?
Adam Rosman, MD
University of Chicago Booth School of Business, Class of 2020
[email protected]

Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.
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