swerve wrote:Machine M and Machine N working alone at their constant rates, non-stop, produced 6000 and 8000 nails respectively. Did machine M work longer than machine N?

1) Machine N produces 2000 more nails than machine M in one hour when each machine work at its constant rate.
2) Machine N produces twice as much as machine M in one hour when each machine work at its constant rate.

Statement 1:
Case 1: N = 4000 nails per hour, M = 2000 nails per hour
Since N's rate = 4000 nails per hour, the time for N to produce 8000 nails = 8000/4000 = 2 hours.
Since M's rate = 2000 nails per hour, the time for M to produce 6000 nails = 6000/2000 = 3 hours.
In this case, M works longer than N, so the answer to the question stem is YES.

Case 2: N = 12000 nails per hour, M = 10000 nails per hour
Since N's rate = 12000 nails per hour, the time for N to produce 8000 nails = 8000/12000 = 2/3 hour = 40 minutes.
Since M's rate = 10000 nails per hour, the time for M to produce 6000 nails = 6000/10000 = 3/5 hour = 36 minutes
In this case, N works longer than M, so the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
In other words, N is twice as fast as M.
If N and M were to work for the same amount of time, then N's 8000-nail production would imply a 4000-nail production for M.
Since M actually produces 6000 nails -- more than 4000 -- M must work for LONGER than N.
Thus, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.