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16 Aug 2026, 19:00
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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.
(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.
16 Aug 2026, 20:19
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Together A + B produce 200 widgets in 4 hours.
So combined rate = 200/4 = 50 widgets/hour.
We need A's rate.
(1) B produces 50 widgets in 5 hours.
B's rate = 50/5 = 10 widgets/hour.
A + B = 50
A + 10 = 50
A = 40 widgets/hour.
Time for A to produce 200 = 200/40 = 5 hours.
So (1) is sufficient.
(2) A produces 4 widgets in the same time B produces 1 widget.
Therefore A's rate = 4B.
We also know:
A + B = 50
So:
4B + B = 50
5B = 50
B = 10
A = 40
Therefore A takes 200/40 = 5 hours.
So (2) is also sufficient.
Answer: D — Each statement alone is sufficient.
So combined rate = 200/4 = 50 widgets/hour.
We need A's rate.
(1) B produces 50 widgets in 5 hours.
B's rate = 50/5 = 10 widgets/hour.
A + B = 50
A + 10 = 50
A = 40 widgets/hour.
Time for A to produce 200 = 200/40 = 5 hours.
So (1) is sufficient.
(2) A produces 4 widgets in the same time B produces 1 widget.
Therefore A's rate = 4B.
We also know:
A + B = 50
So:
4B + B = 50
5B = 50
B = 10
A = 40
Therefore A takes 200/40 = 5 hours.
So (2) is also sufficient.
Answer: D — Each statement alone is sufficient.
it looks both alone are suff D
