Problem Solving

Jim@StratusPrep wrote:Tough question, I could definitely see it as a question. See the figure below. You have 2 sectors each with an area of π and 2 triangles each with an area of 1.

2Ï€ - 2




Let me know if you have questions.
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Brent@GMATPrepNow wrote:

sandipgumtya wrote:"ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region? "
(A)4pi - 1
(B)3pi - 1
(C)2pi - 4
(D)(3pi - 1)/2
(E)2pi-2

Let's apply some ESTIMATION.
We can do so because, unless specified otherwise, the diagrams in Problem Solving questions are drawn to scale.
If we combine the two semi-circles, we get a complete circle with radius 2.
Area of circle = (pi)(r²) = (pi)(2²) = 4(pi) ≈ 4(3) ≈ 12
So, the total area of the two semi-circles is APPROXIMATELY 12

Now, let's ESTIMATE the portion of the semi-circles that's shaded.
Hmmm, looks like ABOUT 1/5 (or perhaps 1/6) is shaded.
1/5 of 12 = 12/5 = 2 2/5 = 2.SOMETHING

Let's check the answer choices to see if any of them are APPROXIMATELY 2.SOMETHING

(A)4pi - 1 ≈ 4(3) - 1 ≈ 11 not even close to 2.SOMETHING
(B)3pi - 1 ≈ 3(3) - 1 ≈ 8 not even close to 2.SOMETHING
(C)2pi - 4 ≈ 2(3) - 4 ≈ 2 looks good. KEEP
(D)(3pi - 1)/2 ≈ [3(3) - 1]/2 ≈ 4 not even close to 2.SOMETHING
(E)2pi-2 ≈ 2(3)-2 ≈ 4 not even close to 2.SOMETHING

Answer: C

Cheers,
Brent