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A circle and a rectangle are there shown as above figure. If the area

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Math Revolution GMAT Instructor
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A circle and a rectangle are there shown as above figure. If the area  [#permalink]

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New post 27 Mar 2016, 00:42
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circle+rectangle.jpg
circle+rectangle.jpg [ 4.95 KiB | Viewed 1016 times ]


A circle and a rectangle are there shown as above figure. If the area of the circle is 100π, what is the perimeter of the rectangle?

1) The one side length of the rectangle except the radius is 20
2) The area shaded is 200-25π


* A solution will be posted in two days.

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Re: A circle and a rectangle are there shown as above figure. If the area  [#permalink]

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New post 27 Mar 2016, 03:04
Area of the circle = 100*pi --> R = 10 = Width

Perimeter of rectangle = 2(Length + Width) --> We have to find the Length.

St1: One side length = 20 --> We know that Width = 10. So the given side is the Length of the rectange. Perimeter can be found out. Sufficient

St2: Area of shaded region = 200 - 25*pi
Area of unshaded region in the rectangle = (1/4)*100*pi = 25*pi
Area of rectangle = 200 - 25pi + 25pi = 200
Length * Width = 200
Length = 200/10 = 20.
Sufficient.

Answer: D
Math Revolution GMAT Instructor
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Re: A circle and a rectangle are there shown as above figure. If the area  [#permalink]

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New post 28 Mar 2016, 21:38
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A circle and a rectangle are there shown as above figure. If the area of the circle is 100π, what is the perimeter of the rectangle?

1) The one side length of the rectangle except the radius is 20
2) The area shaded is 200-25π

Attachment:
perimeter.jpg
perimeter.jpg [ 3.89 KiB | Viewed 901 times ]

As above the picture, suppose one side of the rectangle is a, which makes 1 variable(a). In order to match with the number of equations, you need 1 equation.
For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
1) a=10 unique –> unique and sufficient.
2) a=10 unique -> unique and sufficient.
Thus, the answer is D.
_________________

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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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A circle and a rectangle are there shown as above figure. If the area  [#permalink]

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New post 29 Apr 2016, 10:01
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A circle and a rectangle are there shown as above figure. If the area of the circle is 100π, what is the perimeter of the rectangle?

1) The one side length of the rectangle except the radius is 20
2) The area shaded is 200-25π

Attachment:
perimeter.jpg

As above the picture, suppose one side of the rectangle is a, which makes 1 variable(a). In order to match with the number of equations, you need 1 equation.
For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
1) a=10 unique –> unique and sufficient.
2) a=10 unique -> unique and sufficient.
Thus, the answer is D.



Interesting, can you please elaborate though? I am not sure if I understood your approach completely.

Thanks
Powell Mittra
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Re: A circle and a rectangle are there shown as above figure. If the area  [#permalink]

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New post 12 Sep 2018, 22:54
MathRevolution
please explain the approach
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Re: A circle and a rectangle are there shown as above figure. If the area &nbs [#permalink] 12 Sep 2018, 22:54
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A circle and a rectangle are there shown as above figure. If the area

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