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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9155
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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Difficulty:   65% (hard)

Question Stats: 52% (02:56) correct 48% (03:14) wrong based on 31 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. $$100π$$ $$m^2$$

_________________

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.
Intern  B
Joined: 13 Jun 2019
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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1
Can anybody please explain how answer is 400 $$pi$$ sq m _________________

Shrekey

PS Forum Moderator G
Joined: 18 Jan 2020
Posts: 1089
Location: India
GPA: 4
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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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
Manager  B
Joined: 22 Oct 2018
Posts: 50
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9155
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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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.

Happy Studying !!!
_________________
PS Forum Moderator G
Joined: 18 Jan 2020
Posts: 1089
Location: India
GPA: 4
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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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

Posted from my mobile device
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9155
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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=>

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 $$πr^2 = 400π.$$

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

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