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# If R is the radius of a certain circle, is the area of this circle

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Verbal Forum Moderator
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If R is the radius of a certain circle, is the area of this circle  [#permalink]

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23 Oct 2017, 07:48
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Difficulty:

25% (medium)

Question Stats:

78% (01:05) correct 22% (01:05) wrong based on 50 sessions

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If R is the radius of a certain circle, is the area of this circle greater than the circumference of this circle?

1. 0<R<3
2. The diameter of the circle is greater than 4

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Joined: 02 Sep 2009
Posts: 47161
Re: If R is the radius of a certain circle, is the area of this circle  [#permalink]

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23 Oct 2017, 07:54
Skywalker18 wrote:
If R is the radius of a certain circle, is the area of this circle greater than the circumference of this circle?

1. 0<R<3
2. The diameter of the circle is greater than 4

The question asks: is $$\pi r^2 > 2\pi r$$?
Is $$r > 2$$?

The first statement is NOT sufficient because r can be less as well as more than 2.
The second statement IS sufficient, because it says that r > 2.

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Joined: 07 Feb 2017
Posts: 11
Re: If R is the radius of a certain circle, is the area of this circle  [#permalink]

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23 Oct 2017, 21:02
Bunuel wrote:
Skywalker18 wrote:
If R is the radius of a certain circle, is the area of this circle greater than the circumference of this circle?

1. 0<R<3
2. The diameter of the circle is greater than 4

The question asks: is $$\pi r^2 > 2\pi r$$?
Is $$r > 2$$?

The first statement is NOT sufficient because r can be less as well as more than 2.
The second statement IS sufficient, because it says that r > 2.

what is asked, R>2 ? or R>sqrt(2) ?
Math Expert
Joined: 02 Sep 2009
Posts: 47161
Re: If R is the radius of a certain circle, is the area of this circle  [#permalink]

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23 Oct 2017, 21:19
Dineshrambalaji wrote:
Bunuel wrote:
Skywalker18 wrote:
If R is the radius of a certain circle, is the area of this circle greater than the circumference of this circle?

1. 0<R<3
2. The diameter of the circle is greater than 4

The question asks: is $$\pi r^2 > 2\pi r$$?
Is $$r > 2$$?

The first statement is NOT sufficient because r can be less as well as more than 2.
The second statement IS sufficient, because it says that r > 2.

what is asked, R>2 ? or R>sqrt(2) ?

Why do you think it's $$r > \sqrt 2$$?

Given: $$\pi r^2 > 2\pi r$$.

Reduce by $$\pi r$$ to get $$r > 2$$.
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Re: If R is the radius of a certain circle, is the area of this circle &nbs [#permalink] 23 Oct 2017, 21:19
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