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# If P and Q are sectors in two different circles, what is the perimeter

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
If P and Q are sectors in two different circles, what is the perimeter  [#permalink]

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30 Aug 2018, 04:57
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Difficulty:

35% (medium)

Question Stats:

73% (01:10) correct 27% (00:57) wrong based on 29 sessions

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If P and Q are sectors in two different circles, what is the perimeter of the sector with the smaller area?

(1) The perimeter of the larger sector is 1.25 as large as that of the smaller sector.
(2) The sum of the perimeters is 14π.

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Re: If P and Q are sectors in two different circles, what is the perimeter  [#permalink]

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30 Aug 2018, 05:17
Bunuel wrote:
If P and Q are sectors in two different circles, what is the perimeter of the sector with the smaller area?

(1) The perimeter of the larger sector is 1.25 as large as that of the smaller sector.
(2) The sum of the perimeters is 14π.

Perimeter of the Sector = Length of arc + 2*radius

Question : the perimeter of the sector with the smaller area?

Statement 1: The perimeter of the larger sector is 1.25 as large as that of the smaller sector.

SInce exact values of perimeters are unknown hence

NOT SUFFICIENT

Statement 2: The sum of the perimeters is 14π

We don't know what fraction of this perimeter is shared by sector with smaller area hence

NOT SUFFICIENT

Combining the two statements

If perimeter of smaller are = x
perimeter of bigger area = 1.25x

and x+1.25x = 14π so x may be determined hence

SUFFICIENT

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Re: If P and Q are sectors in two different circles, what is the perimeter   [#permalink] 30 Aug 2018, 05:17
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