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If P, Q and R are the centers of circles P, Q, and R and

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by Gmat_mission » Sat Apr 27, 2019 3:43 am

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If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded?

A. 3/16
B. 1/5
C. 6/25
D. 1/4
E. 3/8

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
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by deloitte247 » Sat May 04, 2019 10:24 pm
The radius of P is twice the radius of Q, and the radius of Q is thrice the radius of R.
If the radius of R=1, then the radius of Q=2, and that of P=4.
$$Area\ of\ circle,\ R=\pi r^2=\pi$$
$$Area\ of\ circle,\ Q=\pi r^2=4\pi$$
$$Area\ of\ circle,\ P=\pi r^2=16\pi$$
$$Area\ of\ shaded\ region=\left(Area\ of\ circle\ P\right)-\left(Area\ of\ circle\ Q\right)+\left(Area\ of\ circle\ R\right)$$
$$Area\ of\ shaded\ region=16\pi-4\pi+\pi=13\pi$$
$$Shaded\ region\ of\ circle\ P=\frac{\left(16\pi-13\pi\right)}{16\pi}=\frac{3\pi}{16\pi}=\frac{3}{16}$$
$$Answer\ =option\ A$$
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by Scott@TargetTestPrep » Mon May 06, 2019 7:07 pm
Gmat_mission wrote:Image
If P, Q and R are the centers of circles P, Q, and R and the points P, Q, R and T all lie on the same line, what portion of circle P is shaded?

A. 3/16
B. 1/5
C. 6/25
D. 1/4
E. 3/8

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
We can let the radius of circles P, Q, and R be 4, 2, and 1, respectively. Therefore, the area of circle P is π(4)^2 = 16π, that of circle Q is π(2)^2 = 4π, and that of circle R is π(1)^2 = π, The area of the shaded region is the difference between the areas of circle Q and circle R. Therefore the area of the shaded region is 4π - π = 3π, and hence 3π/(16π) = 3/16 of circle P is shaded.

Answer: A

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