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 =

2π

r 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