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03 Aug 2026, 08:22
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At the start of a data-conversion job, two servers, Alpha and Beta, were assigned to process the same batch of files. Both servers began processing at the same time, but Alpha was taken offline after 3 hours. Was the number of additional hours that Beta continued processing by itself before the entire batch was completed more than 3 hours?
(1) During the 3 hours that Alpha was running, it processed \(\frac{1}{3}\) of the batch.
(2) Beta would need 9 hours to process the entire batch by itself.
(1) During the 3 hours that Alpha was running, it processed \(\frac{1}{3}\) of the batch.
(2) Beta would need 9 hours to process the entire batch by itself.
03 Aug 2026, 08:22
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Official Solution:
At the start of a data-conversion job, two servers, Alpha and Beta, were assigned to process the same batch of files. Both servers began processing at the same time, but Alpha was taken offline after 3 hours. Was the number of additional hours that Beta continued processing by itself before the entire batch was completed more than 3 hours?
(1) During the 3 hours that Alpha was running, it processed \(\frac{1}{3}\) of the batch.
Alpha handled \(\frac{1}{3}\) of the batch before going offline. That means Beta handled the other \(\frac{2}{3}\) of the batch. But knowing that Beta handled \(\frac{2}{3}\) of the work is still not enough, because we do not yet know how fast Beta processes files. Not sufficient.
(2) Beta would need 9 hours to process the entire batch by itself.
So this tells us Beta’s full-job time, but it does not tell us what share of the batch Beta actually processed in this situation. Not sufficient.
(1)+(2):
From (1), Beta processed \(\frac{2}{3}\) of the batch.
From (2), Beta needs 9 hours for the whole batch, so Beta needs \(9 * \frac{2}{3} = 6\) hours to process \(\frac{2}{3}\) of the batch.
Those 6 hours include the first 3 hours, because Beta was already working while Alpha was still online. So the time Beta worked alone was \(6 - 3 = 3\) hours. The answer to the question is no. Sufficient.
Answer: C
At the start of a data-conversion job, two servers, Alpha and Beta, were assigned to process the same batch of files. Both servers began processing at the same time, but Alpha was taken offline after 3 hours. Was the number of additional hours that Beta continued processing by itself before the entire batch was completed more than 3 hours?
(1) During the 3 hours that Alpha was running, it processed \(\frac{1}{3}\) of the batch.
Alpha handled \(\frac{1}{3}\) of the batch before going offline. That means Beta handled the other \(\frac{2}{3}\) of the batch. But knowing that Beta handled \(\frac{2}{3}\) of the work is still not enough, because we do not yet know how fast Beta processes files. Not sufficient.
(2) Beta would need 9 hours to process the entire batch by itself.
So this tells us Beta’s full-job time, but it does not tell us what share of the batch Beta actually processed in this situation. Not sufficient.
(1)+(2):
From (1), Beta processed \(\frac{2}{3}\) of the batch.
From (2), Beta needs 9 hours for the whole batch, so Beta needs \(9 * \frac{2}{3} = 6\) hours to process \(\frac{2}{3}\) of the batch.
Those 6 hours include the first 3 hours, because Beta was already working while Alpha was still online. So the time Beta worked alone was \(6 - 3 = 3\) hours. The answer to the question is no. Sufficient.
Answer: C
