CONCEPT: Distance travelled by Wheel in 1 revolution = Circumference of Wheel = 2 *(Pi)* Radius
and Total Distance covered by Wheel = No. of Revolutions made to cover that Distance * (2*(Pi)*r)

Statement 1: At the moment Sue and Nancy crossed paths, Sue had travelled 60 feet with the wheelbarrow.

Speeds of Sue / Speeds of Nancy = 2/3

Speeds of Sue / Speeds of Nancy = Distance of Sue / Distance of Nancy

i.e. Distance travelled by Nancy in same time = (3/2)*60 = 90 feet

i.e. Total Distance between X and Y = 60 + 90 = 150 Feet

But This doesn't provide us the information about how many revolutions does the wheel takes to cover total or any part of distance

Hence NOT SUFFICIENT


Statement 2: The total number of wheel revolutions during Sue's trip from X to Y was 75

But This doesn't provide us the information about Total distance travelled by the wheel in 75 Revolutions

Hence NOT SUFFICIENT

Combining the two statements

Total Distance = 150 feet (Calculated from statement 1)
Total Revolutions made by wheel to cover total distance = 75

i.e. 150 = 75 * (2*pi*r)

i.e. Radius of wheel, r = 1/(pi)

SUFFICIENT

Answer: Option
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MANHATTAN GMAT OFFICIAL SOLUTION:

For the wheelbarrow, we can set up a distance formula:
Distance Traveled = (Wheel Circumference) (Number of Wheel Revolution)
Distance Traveled = (2πr) (Number of Wheel Revolutions)

\(\frac{Distance \ Traveled}{(2\pi{r})(Number \ of \ Wheel \ Revolutions)}=r\)

We can rephrase the question from “What is r?” to “What is the distance traveled and the number of wheel revolutions?”

(1) INSUFFICIENT: This provides the distance traveled, but no information about the number of wheel revolutions.

(2) INSUFFICIENT: This gives the number of wheel revolutions, but no information about the total distance from X to Y.

(1) AND (2) SUFFICIENT: If Sue traveled 60 feet at a rate of 2 feet per second, she traveled for 60/2 = 30 seconds before meeting Nancy. During those 30 seconds, Nancy had traveled at a rate of 3 feet per second, for a distance of (3)(30) = 90 feet. The total distance between X and Y is 60 + 90 = 150 feet.

We also know the total number of wheel revolutions that occurred between X and Y, so we have the answer to the rephrased question.

The correct answer is C.
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Circumference * Rev = Total distance covered.

Distance covered by Sue = 60 feet, Time taken = 60/2 = 30 secs.
Distance covered by Nancy in same time = 30 * 3 = 90 feet.

Total D = 60 + 90 = 150 feet.

2 * pi * r * 75 = 150

using I and II, we can get the value of the wheelbarrow radius, hence C