What is the area of the shaded figure?

[gmattesttaker2]

Hello,

Can you please assist with this:

In the figure above, circle C is tangent to rectangle ABCD at points E, F, and G.
What is the area of the shaded figure?

(1) AB = 4
(2) The perimeter of rectangle ABCD is 20.

OA: C

Thanks,
Sri

[Uva@90]

Sri,
We have to find the area of the shaded region.

Area of the shaded region = Area of Rectangle - Area of Circle
Area of Rectangle = l*h
Area of Circle = 3.14*r^2

So, In order to find Area of the shaded region we need to know l,h,r
Now, we can rephrase the question,
What is the value of l,h,r ?

Statement 1: AB = 4
We know that h = 4 and Diameter of circle is 4 so radius = 2
we know only h,r. We don't know about L .Hence Insufficient.

Statement 2: The perimeter of rectangle ABCD is 20.
2(l+h) = 20 => l+h = 10
Here, l and h can take any value 1,9 or 2,8 or3,7 ....
We can't say single value. Hence Insufficient.

Combine 1 and 2:
we can say h = 4 and r = 2 from statement 1 and
therefore l should be 6.
we know, h,r,l. Hence Sufficient.

Answer is C

Regards,
Uva.

[theCodeToGMAT]

To find: area of shaded region

Statement 1:
AB = 4
We have no information about the AD
INSUFFICIENT

Statement 2:
Perimeter = 20
We don't have exact information about AB & AD..
So, we cannot comment on the shaded region
INSUFFICIENT

Combining...
AB = 4
AD = (20 - 2*4)/2 = 6
Radius of circle = 2
We can find out area of shaded region by:
Area of Rectangle - Area of circle.
SUFFICIENT

Answer [spoiler]{C}[/spoiler]

[[email protected]]

Sri,

Uva@90 has written up a perfect explanation for this question. For future reference, here are the things you should think in these types of situations:

1) In a DS question, you should NOT trust the picture; instead, trust the facts/vocabulary/numbers that are in the wording of the question.
2) Any time a circle is involved, pay very careful attention to how the radius effects the question/math/other shapes.

GMAT assassins aren't born, they're made,
Rich