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31 Jul 2025, 08:18
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20 machines, each working at a different constant rate, work to complete a certain job. Each day, exactly 2 machines are assigned to work, and no pair of machines works together more than once. After all such unique pairs have worked once, all 20 machines work together for 6 additional days to complete the job. If all 20 machines had worked together from the beginning, in how many days would the job have been completed?
A. 19
B. 25
C. 26
D. 190
E. 196
A. 19
B. 25
C. 26
D. 190
E. 196
31 Jul 2025, 08:18
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Official Solution:
20 machines, each working at a different constant rate, work to complete a certain job. Each day, exactly 2 machines are assigned to work, and no pair of machines works together more than once. After all such unique pairs have worked once, all 20 machines work together for 6 additional days to complete the job. If all 20 machines had worked together from the beginning, in how many days would the job have been completed?
A. 19
B. 25
C. 26
D. 190
E. 196
Each machine worked 1 day in a pair with each of the remaining 19 machines. Hence, each machine worked for 19 days in pairs.
After all unique pairs had worked once, all 20 machines worked together for 6 more days.
So, each machine worked a total of 19 + 6 = 25 days.
Thus, if all machines had worked together from the beginning, they would have completed the job in 25 days.
Answer: B
20 machines, each working at a different constant rate, work to complete a certain job. Each day, exactly 2 machines are assigned to work, and no pair of machines works together more than once. After all such unique pairs have worked once, all 20 machines work together for 6 additional days to complete the job. If all 20 machines had worked together from the beginning, in how many days would the job have been completed?
A. 19
B. 25
C. 26
D. 190
E. 196
Each machine worked 1 day in a pair with each of the remaining 19 machines. Hence, each machine worked for 19 days in pairs.
After all unique pairs had worked once, all 20 machines worked together for 6 more days.
So, each machine worked a total of 19 + 6 = 25 days.
Thus, if all machines had worked together from the beginning, they would have completed the job in 25 days.
Answer: B
Aakash7
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07 Aug 2025, 23:42
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I did not quite understand the solution. The language of the question seems misleading. It says each day exactly 2 machines are set to work.
But the explanation directs as, each day all machines in unique pairs are set to work.
Please explain.
But the explanation directs as, each day all machines in unique pairs are set to work.
Please explain.
