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In the figure above, arcs PR and QS are semicircles with ce

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In the figure above, arcs PR and QS are semicircles with ce [#permalink]  18 Jun 2019, 21:58
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#GREpracticequestion In the figure above, arcs PR and QS .jpg [ 49.47 KiB | Viewed 1424 times ]

In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what" is the perimeter of the shaded region?

(A) $$5\pi + 5$$

(B) $$5\pi + 15$$

(C) $$10\pi + 10$$

(D) $$10\pi + 15$$

(E) $$100\pi$$
[Reveal] Spoiler: OA

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Re: In the figure above, arcs PR and QS are semicircles with ce [#permalink]  19 Jun 2019, 09:35
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Quote:
In the figure above, arcs PR and QS are semicircles with centers at Q and R respectively. If PQ = 5, what" is the perimeter of the shaded region?

In GRE geometry questions, always look for logical estimation opportunities and solve for the easy shape or value first.

Then, we can solve of the straight portion of the figure which is PQ + RS = 10.

Look to the answer choices to see which include the value of 10 since the circle must include π.

Only Choice C includes the necessary value of 10, so select Choice C without even needing to spend the time calculating the included circumference which would have been 2πr = 2π x 5 = 10π.
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Re: In the figure above, arcs PR and QS are semicircles with ce [#permalink]  21 Nov 2020, 06:07
I am unclear about the math, if anybody can give an explanation about it.
GRE Prep Club Tests Editor
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GRE 1: Q169 V168
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Re: In the figure above, arcs PR and QS are semicircles with ce [#permalink]  22 Nov 2020, 09:07
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Kafi22 wrote:
I am unclear about the math, if anybody can give an explanation about it.

The formula for perimeter of a semicircle = diameter + πr.

Since the radius for either semicircle is 5, then the the perimeter of a single semicircle = 10 + 5π.

However, there are two semicircle arcs included in the shaded figure, so the shaded perimeter = 10 + 5π + 5π = 10 + 10π, choice C.

Of course, I stand by the earlier estimation as possibly a more efficient path to solving on the actual GRE.
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Stefan Maisnier

Re: In the figure above, arcs PR and QS are semicircles with ce   [#permalink] 22 Nov 2020, 09:07
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