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# What is the radius of semicircle S, shown above?

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Math Expert
Joined: 02 Sep 2009
Posts: 64236

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12 Sep 2016, 03:39
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:26) correct 40% (01:18) wrong based on 129 sessions

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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.

Attachment:

T6373.png [ 3.94 KiB | Viewed 1892 times ]

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Director
Joined: 05 Mar 2015
Posts: 936

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12 Sep 2016, 04:01
Bunuel wrote:

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.

Attachment:
T6373.png

Let r be radius so AB=2r then
(1) 2πr/2=100
r=100/π.....sufff
(2) 2πr/2=2r+50π/100....can calculate r...sufff

Ans D
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12 Sep 2016, 08:02
2
rohit8865 wrote:
Bunuel wrote:

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.

Attachment:
T6373.png

Let r be radius so AB=2r then
(1) 2πr/2=100
r=100/π.....sufff
(2) 2πr/2=2r+50π/100....can calculate r...sufff

Ans D

Don't you think there is something wrong in the highlighted line above.

We are given Perimeter of S is 50π % longer. So, it should be something like

πr = 2r(1+π/2). r will cancel out on both sides and we won't be able to find the value of r.

I marked A for the same reason.
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Manager
Joined: 14 May 2014
Posts: 52
Location: India
GMAT 1: 680 Q49 V31
GPA: 3.44

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12 Sep 2016, 09:37
abhimahna wrote:
rohit8865 wrote:
Bunuel wrote:

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.

Attachment:
T6373.png

Let r be radius so AB=2r then
(1) 2πr/2=100
r=100/π.....sufff
(2) 2πr/2=2r+50π/100....can calculate r...sufff

Ans D

Don't you think there is something wrong in the highlighted line above.

We are given Perimeter of S is 50π % longer. So, it should be something like

πr = 2r(1+π/2). r will cancel out on both sides and we won't be able to find the value of r.

I marked A for the same reason.

B states Perimeter of S( pi R + 2R) = (50pi/100)2R + 2R
on solving LHS= RHS so cannot find R
Director
Joined: 05 Mar 2015
Posts: 936

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12 Sep 2016, 10:01
1
abhimahna wrote:
rohit8865 wrote:
Bunuel wrote:

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.

Attachment:
T6373.png

Let r be radius so AB=2r then
(1) 2πr/2=100
r=100/π.....sufff
(2) 2πr/2=2r+50π/100....can calculate r...sufff

Ans D

Don't you think there is something wrong in the highlighted line above.

We are given Perimeter of S is 50π % longer. So, it should be something like

πr = 2r(1+π/2). r will cancel out on both sides and we won't be able to find the value of r.

I marked A for the same reason.

Ah.... thanks Abhi....
silly mistake
+1
Senior Manager
Joined: 26 Jun 2017
Posts: 384
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)

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24 May 2018, 08:04
Bunuel wrote:

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.

Attachment:
T6373.png

----------

(2) The perimeter of S is (50π)% longer than line segment AB.
--------------
Really? GMAT can ask something like that?
Manager
Joined: 29 Sep 2016
Posts: 111

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14 Sep 2019, 20:47
Ans D[/quote]

Don't you think there is something wrong in the highlighted line above.

We are given Perimeter of S is 50π % longer. So, it should be something like

πr = 2r(1+π/2). r will cancel out on both sides and we won't be able to find the value of r.

I marked A for the same reason.[/quote]
Ah.... thanks Abhi....
silly mistake
+1 :wink:[/quote]

However, the approach is ok, the equation for perimeter of semicircle isn't right.
Perimeter of semi circle is
(2r+πr) not (πr)
Re: What is the radius of semicircle S, shown above?   [#permalink] 14 Sep 2019, 20:47