A and B ran, at their respective constant rates, a race

rakeshd347 wrote:A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

OA is A

This question is harder than what you're likely to see on the GMAT, but it offers a useful take-away:
When faced with a hard PS problem, consider PLUGGING IN THE ANSWERS.
Here, the answers represent B's rate in meters per second.

In the first heat, B gets a head start of 48 meters.
Thus, the distance traveled by B in the first heat = 480-48 = 432 meters.
In the second heat, B gets a head start of 144 meters.
Thus, the distance traveled by B in the second heat = 480-144 = 336 meters.

In each heat, the difference between B's number of seconds and A's number of seconds is an INTEGER VALUE:
1/10 of a minute = 6 seconds in the first heat.
1/30 of a minute = 2 seconds in the second heat.
Thus, the correct rate for B must be a factor of both of B's distances (432 and 336).
Only A and C satisfy this constraint.

Answer choice C: B's rate = 16 meters per second
First heat:
Time for B to travel 432 meters = d/r = 432/16 = 27 seconds.
Since A wins by 6 seconds, A's time to travel the entire 480 meters = 27-6 = 21 seconds.
Since A's rate (21 seconds) is not a factor of A's distance (480 meters), eliminate C.

The correct answer is A.

Answer choice A: B's rate = 12 meters per second.
First heat:
Time for B to travel 432 meters = d/r = 432/12 = 36 seconds.
Since A wins by 6 seconds, A's time to travel the entire 480 meters = 36-6 = 30 seconds.
Thus, A's rate = d/t = 480/30 = 16 meters per second.

Second heat:
Time for B to travel 336 meters = d/r = 336/12 = 28 seconds.
Time for A to travel the entire 480 meters = d/r = 480/16 = 30 seconds.
Time difference = 30-28 = 2 seconds.
Success!

rakeshd347 wrote:A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

OA is A

Are these sort of questions common on gmat. What would you rate the difficulty level of these questions if they are common on GMAT.

Alternate approach:

Head start in the second heat - head start in the first heat = 144-48 = 96 meters.
Thus, B travels an additional 96 meters in the first heat.

In the second heat, B travels for 2 seconds LESS than A (with the result that B WINS by 2 seconds).
In the first heat, B travels for 6 seconds MORE than A (with the result that B LOSES by 6 seconds).
Since 2+6 = 8, B travels for 8 seconds LONGER in the first heat than he does in the second heat.

Since in these 8 seconds B travels an additional 96 meters, his rate = d/t = 96/8 = 12 meters per second.

The correct answer is A.