How long would it take for ball moving in a straight line to travel 24

Question

How long would it take for ball moving in a straight line to travel 246 meters?
 
(1) The ball travels 43 meters per minute.
(2) The ball completed one-fourth the trip in 78 rotations.

RMD007 · Answer

We know distance = 246mtrs. To find time, we need speed.

Statement 1: Speed - 43mtrs/min Sufficient.

Statement 2: Rotations are given, we need radius of the ball to determine the distance covered in 78 rotations. Insufficient.

IMO A.

Mo2men · Answer

How long would it take for ball moving in a straight line to travel 246 meters?
 
(1) The ball travels 43 meters per minute.

We know total distance and speed. So T =D/v

Sufficient

(2) The ball completed one-fourth the trip in 78 rotations.

We do not know anything about the rest of distance.

Insufficient

Answer: A

Mo2men · Answer

Dear Bunuel,

In statement 2, how can I rotation to distance completed? Isn't one fourth equals to 61.5 meters? When statement 2 will sufficient?

Thanks

Bunuel · Answer

(2) means that 61.5 meters is completed in 78 rotations.

Mo2men · Answer

Thanks a lot for your support.

How can I calculate rotational speed? Can you guide me to GMAT lesson or questions?

DmitryFarberMPrep · Answer

Mo2men , I don't know of any GMAT-specific resources on this topic, in part because there's very little you need to know. Basically, a rolling ball or wheel will cover a distance equal to its circumference every time it makes a rotation. So if you know how far it goes in a rotation, then you can find circumference, radius, etc. Similarly, if you know the radius, you can find the circumference and see how far it goes in a rotation. That's really all you have to know.

So if a bike wheel has a radius of 2', and if it goes through 50 full rotations, you can calculate the distance traveled. Distance = (circumference) (# of rotations) = (4pi')(50) = 200(pi)'

Looking at statement 2 of this problem, we actually can find the radius of the ball using the same formula: Distance traveled = (circumference) (# of rotations). We know the ball went 1/4 of 246m in 76 rotations. 61.5 = (2*pi*r) (76) We can solve for r if we really want: r = 61.5/(152pi). The numeric answer, as you can imagine, is not pretty. In any case, we don't want to do this. First, we have no need for the radius. We already know the distance traveled. What we want is the time, and statement 2 gives us no information about time at all. That alone makes it insufficient, with no need for any of the math we just did!

Notice that even if statement 2 did tell us how long the ball took to get 1/4 of the way, it would still be insufficient unless it told us that the ball continued at that pace for the rest of the trip. Be careful never to assume a constant rate if that isn't stipulated! (We can figure out the number of rotations for the whole trip, since it's safe to assume that the ball isn't changing size over the trip. However, we've already established that the number of rotations tells us nothing about time.)

Bunuel · Answer

Mo2men · Answer

Thanks a lot for detailed explanation

bumpbot · Answer

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How long would it take for ball moving in a straight line to travel 24

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