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# If P and Q are circular regions, what is the radius of the smaller of

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
If P and Q are circular regions, what is the radius of the smaller of  [#permalink]

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12 Sep 2018, 00:45
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Difficulty:

35% (medium)

Question Stats:

67% (00:55) correct 33% (00:33) wrong based on 14 sessions

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If P and Q are circular regions, what is the radius of the smaller of these regions?

(1) The sum of the radii of the two regions is 20.
(2) The circumference of the larger circle is equal to 40π minus the circumference of the smaller circle.

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Re: If P and Q are circular regions, what is the radius of the smaller of  [#permalink]

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12 Sep 2018, 04:52
Bunuel wrote:
If P and Q are circular regions, what is the radius of the smaller of these regions?

(1) The sum of the radii of the two regions is 20.
(2) The circumference of the larger circle is equal to 40π minus the circumference of the smaller circle.

Question: If P and Q are circular regions, what is the radius of the smaller of these regions?

To answer this question we only need the radius of the smaller circle of these two .

Statement 1: The sum of the radii of the two regions is 20

Smaller radius can be anything less than 10 hence no specific value for the smaller radius hence

NOT SUFFICIENT

Statement 2: The circumference of the larger circle is equal to 40π minus the circumference of the smaller circle.

2πR = 40π - 2πr
i.e. R+r = 20

NOT SUFFICIENT

Combining the two statements

Both statements are giving us the same information hence no further deduction after combining them hence

NOT SUFFICIENT

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Re: If P and Q are circular regions, what is the radius of the smaller of   [#permalink] 12 Sep 2018, 04:52
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