A circle has the same area with a rectangle. What is the circumference

Question

A circle has the same area with a rectangle. What is the circumference of the circle?
1) The perimeter of the rectangle is 18
2) The area of the rectangle is 20

*An answer will be posted in 2 days.

chetan2u · Answer

Area of circle = Area of rectangle..

1) The perimeter of the rectangle is 18 
Different Area can be possible...
say the sides are 8 and 1.. P = 2(8+1)=18, and A = 8*1 = 8
say the sides are 7 and 2.. 2(7+2)=18, and A = 7*2 = 14
So each of them will give a different circumference of circle
Insuff

2) The area of the rectangle is 20 
Area of circle = 20....
so  \pi*r^2 = 20 ..... we can find  2*\pi*r 
suff

B

adiagr · Answer

Statement 1

Perimeter of rectangle is 18, so a+b is known but I do not know the value of ab.
a+b = 9

a = 6 b =3, ab = 18
a=9, b=1, ab=9.

so different areas will result. Not sufficient.

Taking Statement (2)
 Unique value for area is known. 
If I have unique area of a circle, then I can get the radius and then I can get circumference. So sufficient.

B is the answer.

MathRevolution · Answer

We can modify the original condition and the question. The area of the circle and the area of the rectangle are same. Hence, since it is asking for the circumference of the circle, we only have to know the area of the circle (which is same as the area of the rectangle). So, the correct answer is B.

- 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.

Kinshook · Answer

Given: A circle has the same area with a rectangle. 
Asked: What is the circumference of the circle?

1) The perimeter of the rectangle is 18
2(l+b) = 18
l + b = 9
Since there may be many different values for area of the rectangle (lb) 
NOT SUFFICIENT

2) The area of the rectangle is 20
 \pi rˆ2 = 20 
 r = \sqrt{20/pi} 
Circumference =  2\pi r = 2\pi \sqrt{20/pi} = 4 \sqrt{5pi} 
SUFFICIENT

IMO B

A circle has the same area with a rectangle. What is the circumference

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GMAT Data Sufficiency (DS) Questions

A circle has the same area with a rectangle. What is the circumference

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