"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
Pl find attached image.
I am getting C as ans.Pl confirm if I am right.
Are these type of qus likely to show up in GMAT?
Pl help.
Geometry Prob
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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 2.
2Ï€ - 4
Let me know if you have questions.
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2Ï€ - 4
Let me know if you have questions.
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Last edited by Jim@StratusPrep on Sun Jul 12, 2015 8:04 am, edited 1 time in total.
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Ha, yup. Made the change. Thanks.
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Let's apply some ESTIMATION.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
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
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@Brent:Like ur approach.But how r u estimating the shaded area to be 1/5 of total.pl explain.Can we expect such question in GMAT?Brent@GMATPrepNow wrote:Let's apply some ESTIMATION.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
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
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Take 1 semi-circle, and examine the half of it (the part that has the shaded portion).sandipgumtya wrote: @Brent:Like ur approach.But how r u estimating the shaded area to be 1/5 of total.pl explain.Can we expect such question in GMAT?
Does the shaded portion take up half of that portion of the circle?
No. So, the shaded portion takes up less than 1/4 of the semi-circle.
If you're okay with this conclusion, we can answer the question.
We're saying that LESS THAN 1/4 of the figure is shaded.
1/4 of 12 = 3
So, the area of the shaded figure is LESS THAN 3
Check the answer choices (using approximation).
Only answer choice C is less than 3.
Cheers,
Brent
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