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# Given two circles, what is the difference in the two areas?

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Given two circles, what is the difference in the two areas?  [#permalink]

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11 Sep 2018, 03:08
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:10) correct 50% (01:12) wrong based on 12 sessions

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Given two circles, what is the difference in the two areas?

(1) The radii of the two circles have a difference of 5.
(2) The circumferences of the two circles have a difference of 10π.

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Re: Given two circles, what is the difference in the two areas?  [#permalink]

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11 Sep 2018, 04:27
Bunuel wrote:
Given two circles, what is the difference in the two areas?

(1) The radii of the two circles have a difference of 5.
(2) The circumferences of the two circles have a difference of 10π.

Question: what is the difference in the two areas?

Difference of areas = $$π(r_1^2 - r_2^2) = π(r_1-r_2)*(r_1+r_2)$$

Statement 1: The radii of the two circles have a difference of 5

This gives us$$(r_1-r_2)=5$$ but the sum of the radie is unknown hence

NOT SUFFICIENT

Statement 2: he circumferences of the two circles have a difference of 10π

This gives us$$2π(r_1-r_2)=10π$$ but the sum of the radie is unknown hence

NOT SUFFICIENT

Combining the two statements

We only have difference of the radie but not the sum of them hence

NOT SUFFICIENT

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Re: Given two circles, what is the difference in the two areas?   [#permalink] 11 Sep 2018, 04:27
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