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# A circular swimming pool is surrounded by a wall with a height of 2m.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9018
GMAT 1: 760 Q51 V42
GPA: 3.82
A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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Updated on: 23 May 2020, 08:58
00:00

Difficulty:

65% (hard)

Question Stats:

52% (03:02) correct 48% (03:04) wrong based on 27 sessions

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[GMAT math practice question]

A circular swimming pool is surrounded by a walk with a width of 2m. The area of the walk is 21% of the area of the swimming pool. What is the area of the swimming pool?

A. $$400π$$ $$m^2$$
B. $$300π$$ $$m^2$$
C. $$250π$$ $$m^2$$
D. $$200π$$ $$m^2$$
E. $$100π$$ $$m^2$$

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"Only $79 for 1 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 22 May 2020, 05:28. Last edited by MathRevolution on 23 May 2020, 08:58, edited 1 time in total. Senior Manager Joined: 18 Jan 2020 Posts: 372 Location: India GPA: 4 Re: A circular swimming pool is surrounded by a wall with a height of 2m. [#permalink] ### Show Tags 22 May 2020, 05:43 Sir, kindly check the height of wall. Are you sure it's not 1m? Because the last value I m getting for r(h+r)=42 And if h is 2, r will be of some imaginary value. Kindly revert. Posted from my mobile device Intern Joined: 22 Oct 2018 Posts: 34 Re: A circular swimming pool is surrounded by a wall with a height of 2m. [#permalink] ### Show Tags 22 May 2020, 07:44 MathRevolution wrote: [GMAT math practice question] A circular swimming pool is surrounded by a wall with a height of 2m. The area of the wall is 21% of the area of the swimming pool. What is the area of the swimming pool? A. 400π m^2 B. 300πm^2 C. 250πm^2 D. 200πm^2 E. 100πm^2 This question seems incomplete or isn't worded properly. Can someone help Intern Joined: 13 Jun 2019 Posts: 11 Re: A circular swimming pool is surrounded by a wall with a height of 2m. [#permalink] ### Show Tags 22 May 2020, 21:34 1 Can anybody please explain how answer is 400 $$pi$$ sq m _________________ Shrekey Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9018 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: A circular swimming pool is surrounded by a wall with a height of 2m. [#permalink] ### Show Tags 23 May 2020, 09:00 SiddharthR wrote: MathRevolution wrote: [GMAT math practice question] A circular swimming pool is surrounded by a wall with a height of 2m. The area of the wall is 21% of the area of the swimming pool. What is the area of the swimming pool? A. 400π m^2 B. 300πm^2 C. 250πm^2 D. 200πm^2 E. 100πm^2 This question seems incomplete or isn't worded properly. Can someone help There were mistakes in words. They are fixed now. The words "wall" and "height" should be fixed with "walk" and "width", respectively. Sorry about the mistakes. Happy Studying !!! _________________ 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$79 for 1 month Online Course"
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Senior Manager
Joined: 18 Jan 2020
Posts: 372
Location: India
GPA: 4
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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23 May 2020, 09:13
Let the radius of walk with the swimming pool in between = r+2
Area of whole area ( swimming pool+ walk) = π(r+2)^2

Given: area of walk is 21% of area of swimming pool.

Area of walk = π(r+2)^2 - πr^2
Therefore,
π(r+2)^2 - πr^2 = 21/100(πr^2)
π{(r+2)^2 - r^2}=π{21/100(r^2)}
(r^2+4+4r)- r^2={21/100(r^2)
4+4r=21/100(r^2)
400+400r=21(r^2)
21(r^2)-400r-400=0
21(r^2)-420r+20r-400=0
21r(r-20)+20(r-20)=0
(r-20)(21r+20)=0
R=20 and -20/21(not possible)
R=20

Area of swimming pool is πr^2
π(20)^2 => 400π

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Math Revolution GMAT Instructor
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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24 May 2020, 17:14
=>

Assume the radius of the swimming pool is $$r$$.

Then the area of the wall is $$2πr·2 = 4πr.$$

Since we have $$4πr = (\frac{21}{100}) πr^2,$$ we have $$21r^2 – 400r + 400 = 0$$ or $$(21r + 20)(r - 20) = 0.$$

Thus, we have $$r = 20.$$

Then, the area of the swimming pool is $$πr^2 = 400π.$$

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Re: A circular swimming pool is surrounded by a wall with a height of 2m.   [#permalink] 24 May 2020, 17:14