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30 Apr 2025, 02:28
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Machine A, operating at a constant rate, can process a 900-unit order in 36 minutes. How many minutes would it take to process the order if Machine A and Machine B worked together at their respective constant rates?
(1) Machine A processes twice as many units as Machine B in the same amount of time.
(2) Machine B takes three times as long to process the entire order alone as it takes both machines working together.
(1) Machine A processes twice as many units as Machine B in the same amount of time.
(2) Machine B takes three times as long to process the entire order alone as it takes both machines working together.
30 Apr 2025, 02:28
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Official Solution:
Machine A, operating at a constant rate, can process a 900-unit order in 36 minutes. How many minutes would it take to process the order if Machine A and Machine B worked together at their respective constant rates?
Since the rate of Machine A and the size of the job are known, we only need to determine the rate of Machine B to answer the question. Once both rates are known, we can compute the combined rate and the required time. So we focus only on whether B's rate can be determined and avoid unnecessary calculation.
(1) Machine A processes twice as many units as Machine B in the same amount of time.
This gives a direct relationship between their rates: A's rate = 2 * B's rate. Since A's rate is known, we can determine B's rate. Sufficient.
(2) Machine B takes three times as long to process the entire order alone as it takes both machines working together.
This statement implies 3 * B's rate = A's rate + B's rate. From this, we get A's rate = 2 * B's rate. Since A's rate is known, we can determine B's rate. Sufficient.
Answer: D
Machine A, operating at a constant rate, can process a 900-unit order in 36 minutes. How many minutes would it take to process the order if Machine A and Machine B worked together at their respective constant rates?
Since the rate of Machine A and the size of the job are known, we only need to determine the rate of Machine B to answer the question. Once both rates are known, we can compute the combined rate and the required time. So we focus only on whether B's rate can be determined and avoid unnecessary calculation.
(1) Machine A processes twice as many units as Machine B in the same amount of time.
This gives a direct relationship between their rates: A's rate = 2 * B's rate. Since A's rate is known, we can determine B's rate. Sufficient.
(2) Machine B takes three times as long to process the entire order alone as it takes both machines working together.
This statement implies 3 * B's rate = A's rate + B's rate. From this, we get A's rate = 2 * B's rate. Since A's rate is known, we can determine B's rate. Sufficient.
Answer: D
25 Jul 2025, 02:18
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Bunuel
When you say Machine A processes twice as many units as Machine B in the same amount of time., this means that the rate of A is twice the rate of B.
Machine B takes three times as long to process the entire order alone as it takes both machines working together
When a statement says that machine B takes three times as long to process the entire order alone as it takes both machines working. This to me means that the time/duration that it takes machine B to the job alone is thrice the time it takes both machine working together. But you say 3 * B's rate = A's rate + B's rate.
Why do you confuse time with rate???
Thanks in advance!
When you say Machine A processes twice as many units as Machine B in the same amount of time., this means that the rate of A is twice the rate of B.
Machine B takes three times as long to process the entire order alone as it takes both machines working together
When a statement says that machine B takes three times as long to process the entire order alone as it takes both machines working. This to me means that the time/duration that it takes machine B to the job alone is thrice the time it takes both machine working together. But you say 3 * B's rate = A's rate + B's rate.
Why do you confuse time with rate???
Thanks in advance!
