Seeing this problem on first glance, my intuition told me that the answer was D. However, on the GRE it is best not to blindly trust our intuition; we should test our assumptions.

If figure was rectangle, then the area would be: 6 x 10 = 60. However, as the edges are rounded we must subtract them from the total:


So the rectangular figure has an approximate area of 60 - (16 - 4 pi ) = 56.566.

From here, we must subtract the area of the circle contained in the figure in order to determine the area of the shaded portion of the figure. As the figure is not drawn to scale, this will be a range of values.



As the radius of the circle is not specified, it could theoretically be an infinitesimally small. Take for example a circle with a radius of 0.01. The area of the circle would be: (0.01)^2 pi = 0.0003. Even this value subtracted from the area of the rectangular figure would be negligible. Thus, we can say that the Area Max = 56.566

To find the minimum area of the shaded portion of the figure, we set the area of the inner circle to it's maximum value:


Subtracting this value from the area of the rectangular figure we can find the minimum area:

56.566 - 3 pi = 28.292 ----> Area min = 28.292

28.292 < QA < 56.566

QB = 30

As QB falls within QA's range, we can confirm that Answer Choice D is correct.

OA is missing sir !

I had a doubt about so I asked the expert before to post the correct one

Thank you
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