What is the radius of semicircle S, shown above? (1) The perimeter of

Question

https://gmatclub.com/forum/download/file.php?id=61988 What is the radius of semicircle S, shown above? (1) The perimeter of S is 100. (2) The perimeter of S is (50π)% longer than line segment AB. Project DS Butler Data Sufficiency (DS3) For DS butler Questions Click Here 1.png

rajatchopra1994 · Answer

Explanation:

Statement 1: perimeter of S is 100
Perimeter of semicircle = r*(𝜋 + 2)
we can find the r by putting values
Sufficient

Statement 2: perimeter of S is (50π)% longer than line segment AB
AB = 2r
r getting cancelled while solving equation
Not sufficient

IMO-A

sumitkrocks · Answer

Statement (1) The perimeter of S is 100.

only variable is radius; a unique circle is identified 
Sufficient

Statement (2) The perimeter of S is (50π)% longer than line segment AB.
A general condition for a circle same as saying radius is 2*PI*radius 
No unique circle can be identified using this statement

Not sufficient

(A)  is the answer IMO

asishron29181 · Answer

What is the radius of semicircle S, shown above?
Perimeter of semi circle = π*r + 2*r

(1) The perimeter of S is 100.
r( π+2 ) = 100
r = 100/( π+2 )
Sufficient.

(2) The perimeter of S is (50 π)% longer than line segment AB.
r*(π+2 ) = 1.5*π*2r
2πr = 2r
Clearly r cancels out
Not sufficient.

IMO A

CrackverbalGMAT · Answer

The perimeter of a circle or semi circle is based on its radius.(For a circle the perimeter is 2*pi*r and hence pi*r for a semicircle)

Statement 1 says, "The perimeter of S is 100".
It provides us with the radius! 
(sufficient)

Statement 2 says "The perimeter of S is (50π)% longer than line segment AB."
However, there is no information about the length of AB and we DO NOT KNOW if AB is the diameter of the semicircle.
There is no mention observed of a center lying on AB.
(insufficient)

PS-It is important in Geometry questions to not assume anything unless information is provided in the question.
 (option a)

Devmitra Sen
GMAT SME

kantapong · Answer

Find r = ?
1) perimeter = 2r + pi r = 100 => sufficient for finding r
2) 2r + pi r = (1 + 50pi/100)(2r) => r = r (not sufficient)
Ans: A

thelonghalloween · Answer

Let's attempt this without actually solving anything

To start of: perimeter of semicircle S = 2r +  \pi r

Statement 1:
S = 100
2r +  \pi r = 100

1 variable and 1 equation --> Solveable 
 Sufficient

Statement 2: 
(S - 2r)/2r = 50n/100
 \pi r/2r = n/2 
 \pi  = n

Doesn't give any information on r
 Insufficient

So A

errorlogger · Answer

1)2πr = 100
r = 100/2π = 50/π - Sufficient!
2)The comparison is given in percent. Since, there is no defined length of the sides. We can't determine r - Insufficient!
IMO A

What is the radius of semicircle S, shown above? (1) The perimeter of

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