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# If P and Q are circular regions, what is the sum of the two radii?

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Joined: 02 Sep 2009
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If P and Q are circular regions, what is the sum of the two radii?  [#permalink]

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14 Sep 2018, 01:42
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45% (medium)

Question Stats:

75% (01:21) correct 25% (00:59) wrong based on 19 sessions

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If P and Q are circular regions, what is the sum of the two radii?

(1) The sum of the circumferences of the two circles is 30π.
(2) The sum of the areas of the two circles is 125π.

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If P and Q are circular regions, what is the sum of the two radii?  [#permalink]

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14 Sep 2018, 01:53
Bunuel wrote:
If P and Q are circular regions, what is the sum of the two radii?

(1) The sum of the circumferences of the two circles is 30π.
(2) The sum of the areas of the two circles is 125π.

Let radius of first circle = $$r_1$$
Let radius of second circle = $$r_2$$

we need to find
$$r_1 + r_2$$

Statement 1 - The sum of the circumferences of the two circles is 30π

Circumference of circle = 2πr
Hence sum of circumferences = $$2π r_1 + 2π r_2$$
$$2π r_1 + 2π r_2$$ = 30π
Hence,
$$r_1 + r_2$$ = 15

Statement 1 is sufficient

Statement 2 -The sum of the areas of the two circles is 125π

Circumference of circle = $$π(r)^2$$
Hence sum of circumferences = $$π(r_1)^2 + π(r_2)^2$$
$$π(r_1)^2 + π(r_2)^2$$ = 125π
Hence,
$$(r_1)^2 + (r_2)^2$$ = 125

Statement 2 is insufficient

Hence IMO Answer is A

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If P and Q are circular regions, what is the sum of the two radii?   [#permalink] 14 Sep 2018, 01:53
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# If P and Q are circular regions, what is the sum of the two radii?

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