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# How many different-sized circles with positive integer radii have area

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Math Expert
Joined: 02 Sep 2009
Posts: 42604

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28 Nov 2017, 20:02
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73% (00:35) correct 27% (00:59) wrong based on 15 sessions

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How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen
[Reveal] Spoiler: OA

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Kudos [?]: 135673 [0], given: 12706

Manager
Joined: 17 Oct 2016
Posts: 150

Kudos [?]: 38 [0], given: 89

Location: India
Concentration: Operations, Strategy
GPA: 3.7
WE: Design (Real Estate)
Re: How many different-sized circles with positive integer radii have area [#permalink]

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28 Nov 2017, 20:29
B

For radius=6 the area is 113.09>100. Hence only upto 5

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Joined: 22 May 2016
Posts: 1131

Kudos [?]: 403 [0], given: 645

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29 Nov 2017, 15:13
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

I can see potential trouble with area = 100.

Area of circle is $$πr^2$$.

So it must be $$r^2 * 3.14 < 100$$, where r is an integer.

Radii 1, 2, 3, 4, and 5 (25 * 3.14 = approx 78) work.

Radius 6 does not: 36 * 3 = 108, so with 3.14 it would be higher.

Five values satisfy the conditions.

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Re: How many different-sized circles with positive integer radii have area [#permalink]

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01 Dec 2017, 06:54
Bunuel wrote:
How many different-sized circles with positive integer radii have areas less than 100?

(A) Four
(B) Five
(C) Six
(D) Ten
(E) Fifteen

If r = 1, then the area of the circle is π(1)^2 = π.

If r = 2, then the area is π(2)^2 = 4π.

If r = 3, then the area is π(3)^2 = 9π.

If r = 4, then the area is π(4)^2 = 16π.

If r = 5, then the area is π(5)^2 = 25π.

Since π < 4, the area of any of the circles above will be less than 100. However, if r = 6, then the area of the circle will be π(6)^2 = 36π. However, since π > 3, 36π will be greater than 100. Thus, there are five different-sized circles with positive integer radii with area less than 100.

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Re: How many different-sized circles with positive integer radii have area   [#permalink] 01 Dec 2017, 06:54
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# How many different-sized circles with positive integer radii have area

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