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TAGS: Founder  Joined: 18 Apr 2015
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Equilater trinagle PQR is formed by joining [#permalink]
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Expert's post 00:00

Question Stats: 68% (00:44) correct 31% (00:55) wrong based on 147 sessions
Attachment: #GREpracticequestion Equilateral triangle PQR is formed by joining.jpg [ 17.91 KiB | Viewed 3831 times ]

Equilateral triangle PQR is formed by joining center P, Q, and R of the circles. Each pair of circles has exactly one point in common.

 Quantity A Quantity B The perimeter of triangle PQR The circumference of the circle with center Q

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 14 Jan 2019, 14:48, edited 3 times in total.
Edited the OA Manager Joined: 15 Feb 2018
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Re: Equilater trinagle PQR is formed by joining [#permalink]
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A: Let r be the radius of each circle. Each side of the equilateral triangle is 2r, so the perimeter is 6r.

B: Circumference of Q = 2 * 3.14 * r > 6r. Intern Joined: 05 Jun 2017
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Re: Equilater trinagle PQR is formed by joining [#permalink]
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From given info
Rp + Rq = other two sides of the triangle
So, perimeter will be 3(Rp+Rq)
Now we have to compare
3Rp + 3Rq ? 2 Pi Rq

As we don't know the value of Rp so answer can not be determined. Intern Joined: 14 Apr 2018
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Re: Equilater trinagle PQR is formed by joining [#permalink]
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Should the answer be B for this question?
Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

Re: Equilater trinagle PQR is formed by joining [#permalink]
Expert's post
Sorry for the inconvenience. fixed.

regards
_________________
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Re: Equilater trinagle PQR is formed by joining [#permalink]
Yep the answer is b as the triangle is equilateral
Intern Joined: 08 Apr 2018
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Re: Equilater trinagle PQR is formed by joining [#permalink]
Carcass wrote:
Sorry for the inconvenience. fixed.

regards

This is yet to be fixed as the answer placed is B,D. Which exactly is it? Manager Joined: 02 May 2018
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Re: Equilater trinagle PQR is formed by joining [#permalink]
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Emike56 wrote:
Carcass wrote:
Sorry for the inconvenience. fixed.

regards

This is yet to be fixed as the answer placed is B,D. Which exactly is it?

Here's another explanation why. Let's pretend that the radius (r) = 5.
Since the triangle is an equilateral triangle, that means each side of the triangle is 10, or 2 * radius of each circle.

Quantity A = Perimeter of Triangle PQR = 30.
Quantity B = Circumference of Circle with Center Q = 2 * pi * 5. = 10 * 3.14 = 31.4.

Quantity B is greater.

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Re: Equilater trinagle PQR is formed by joining [#permalink]
Ans B
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Re: Equilater trinagle PQR is formed by joining [#permalink]
Agree, the answer is B if the circles are identical but there is nowhere mentioned in the question that the circles have the same radius.

Thanks
Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3676 , given: 12912

Re: Equilater trinagle PQR is formed by joining [#permalink]
Expert's post
The assumption is wrong: the stem says that PQR is an equilateral triangle, which means all sides are equal in length.

So, if one side is 10 (for instance) the other two are 10 as well.

If one side is 10, half of it is 5, which is the radius of all 3 circles. Is the radius is equal, the 3 areas are equal as well.

Hope now is clear.

Regards
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Re: Equilater trinagle PQR is formed by joining [#permalink]
How do you know all Circles are equal?

Posted from my mobile device Founder  Joined: 18 Apr 2015
Posts: 13891
GRE 1: Q160 V160 Followers: 313

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Re: Equilater trinagle PQR is formed by joining [#permalink]
Expert's post
Because the equilateral triangle has 3 side equal in lenght

The same side, added up. is the two radii of a circle.

Therefore the circles must be equal
_________________ Re: Equilater trinagle PQR is formed by joining   [#permalink] 31 Aug 2020, 09:46
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