Correct Answer : DGiven:
Combined Rate = 200 widgets / 4 hours = 50 widgets/hour
Target: Time taken by Machine A alone to produce 200 widgets (Need Rate_A)
Statement (1): Machine B takes 5 hours to produce 50 widgets.
Rate_B = 50 widgets / 5 hours = 10 widgets/hour
Since Rate_A + Rate_B = 50:
Rate_A + 10 = 50 ==> Rate_A = 40 widgets/hour
Time for Machine A = 200 / 40 = 5 hours.
Sufficient.
Statement (2): Machine A produces 4 widgets in the time Machine B produces 1 widget.
This gives the ratio: Rate_A = 4 * Rate_B
Substitute this into the combined rate equation:
(4 * Rate_B) + Rate_B = 50
5 * Rate_B = 50 ==> Rate_B = 10 widgets/hour
Rate_A = 4 * 10 = 40 widgets/hour
Time for Machine A = 200 / 40 = 5 hours.
Sufficient.
Each statement alone is sufficient.
--------------------------------------------------Difficulty Level: Easy (Level 1)GMAT Focus Benchmark: Q75 - Q78 (~40th - 55th percentile)Target Score Range: 505 - 555Bunuel
Working together, Machine A and Machine B can produce a total of 200 widgets in 4 hours. How many hours would it take Machine A, working alone, to produce 200 widgets?
(1) Working alone, Machine B takes 5 hours to produce 50 widgets.
(2) Machine A can produce 4 widgets in the same amount of time it takes Machine B to produce 1 widget.