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After running 3,000 meters on a circular path, a runner is at her star

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After running 3,000 meters on a circular path, a runner is at her star [#permalink]

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New post 21 Nov 2017, 23:07
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Question Stats:

43% (00:41) correct 57% (00:52) wrong based on 28 sessions

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After running 3,000 meters on a circular path, a runner is at her starting point. The radius of her circular path could be which of the following?

I. 1,500/π meters
II. 750/π meters
III. 250/π meters

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

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Re: After running 3,000 meters on a circular path, a runner is at her star [#permalink]

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New post 22 Nov 2017, 00:01
Bunuel wrote:
After running 3,000 meters on a circular path, a runner is at her starting point. The radius of her circular path could be which of the following?

I. 1,500/π meters
II. 750/π meters
III. 250/π meters

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III


if r = 1500/π then Circumference is 2πr = 3000....one rotation..possible
if r = 750/π then Circumference is 2πr = 1500....2 rotations..possible
if r = 250/π then Circumference is 2πr = 500....6 rotations..possible

E
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After running 3,000 meters on a circular path, a runner is at her star [#permalink]

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New post 22 Nov 2017, 11:01
Bunuel wrote:
After running 3,000 meters on a circular path, a runner is at her starting point. The radius of her circular path could be which of the following?

I. 1,500/π meters
II. 750/π meters
III. 250/π meters

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

Distance run =
circumference 2πr (of track) *
# of revolutions (# of full laps run)
And D/circumference = # of laps

She ran 3,000 m from start point to start point, in a circle. A possible radius of the track will make the distance she ran evenly divisible by the circumference of the track; even division yields full laps (revolutions).

I. r = 1,500/π meters
πr = 1,500 m
2πr = 3,000 m
3,000m/3,000m = 1 circumference =
One lap around the track. YES

II. r = 750/π meters
πr = 750 m
2πr = 1,500 m
3,000m/1,500 m = 2 "circumferences" =
Two laps around the track. YES

III. 250/π meters
πr = 250 m
2πr = 500 m
3,000m/500 m = 6 "circumferences" =
Six laps around the track. YES

Answer E

Shortcut: any number that is a factor of 3000, as long as it is divided by π, is a possible radius. One exception: 3,000 itself.*

A factor divides evenly into a multiple; the multiple, 3000, divided by any of its factors except itself, will yield full laps. That is, the radius will form a circumference of _____ m = 2πr that divides evenly into 3,000 m

1,500, 750, and 250 are factors of 3,000. All three options, divided by π, are possible radii.

Answer E

*3,000/π m will not work because circumference is 2πr, so she would have run only one-half of a lap.
If r = 3,000/π meters, then
πr = 3,000 m and
2πr = 6,000 m
3,000m/6,000m = 1/2 circumference = 1/2 lap

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After running 3,000 meters on a circular path, a runner is at her star   [#permalink] 22 Nov 2017, 11:01
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