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The area of Circle O is added to its diameter...

by swerve » Thu Jan 11, 2018 7:06 am
The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/Ï€
B. 2
C. 3
D. 4
E. 5

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
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by Brent@GMATPrepNow » Thu Jan 11, 2018 7:21 am
swerve wrote:The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/Ï€
B. 2
C. 3
D. 4
E. 5
Area = πr²
Diameter = 2r
Circumference = 2Ï€r

We can write: πr² + 2r - 2πr = 4
Rearrange and set equal to zero to get: πr² - 2πr + 2r - 4 = 0
Factor IN PARTS: πr(r - 2) + 2(r - 2) = 0
Combine to get: (Ï€r + 2)(r - 2) = 0

So, EITHER πr + 2 = 0 OR r - 2 = 0
If πr + 2 = 0, then r = -2/π (not possible)
If r - 2 = 0, then r = 2 (perfect!)

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by GMATWisdom » Thu Jan 11, 2018 8:23 am
swerve wrote:The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the radius of Circle O?

A. 2/Ï€
B. 2
C. 3
D. 4
E. 5

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer and I would like to know how to solve it in less than 2 minutes. I need your help. Thanks.
I give you a method which will solve it in just a few seconds:
As there is no π term in the net result that means the π terms of area and circumference gets totally eliminated when we subtract circumference from the area. Which means the area of the circle must be equal to the circumference.
Then πr^2+2r-2πr=4
Therefore 2r=4 (because πr^2=2πr)
or r=2
Hence option B
You may verify also by making πr^2=2πr which also gives r=2
Happy ?
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