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14 Jan 2025, 15:06
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The number of jobs
completed by machine J: 63 The number of jobs completed by
machines K and L working together
and with no other machines: 42
completed by machine J: 63 The number of jobs completed by
machines K and L working together
and with no other machines: 42
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
62% (03:11) correct
38%
(03:12)
wrong
based on 664
sessions
History
Date
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Not Attempted Yet
Working together, machine J, machine K, and machine L can complete a job in 12 minutes. Working alone, machine J can complete a job in 20 minutes. Machine J worked alone for a given amount of time. Then, machines K and L worked together, and with no other machine, for the same amount of time.
In the table below, select two numbers that are consistent with the information that is given. In the first column, select the row that shows the number of jobs completed by machine J working alone, and in the second column, select the row that shows the number of jobs completed by machines K and L working together and with no other machines. Make exactly one selection for each column.
In the table below, select two numbers that are consistent with the information that is given. In the first column, select the row that shows the number of jobs completed by machine J working alone, and in the second column, select the row that shows the number of jobs completed by machines K and L working together and with no other machines. Make exactly one selection for each column.
|
The number of jobs completed by machine J |
The number of jobs completed by machines K and L working together and with no other machines |
|
| 24 | ||
| 42 | ||
| 60 | ||
| 63 | ||
| 84 | ||
| 96 |
ShowHide Answer
Official Answer
The number of jobs
completed by machine J: 63 The number of jobs completed by
machines K and L working together
and with no other machines: 42
completed by machine J: 63 The number of jobs completed by
machines K and L working together
and with no other machines: 42
15 Jan 2025, 07:00
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Bookmarks
1. Let the speeds of the three machines be j, k, and l.
2. All three machines do one job for 12 minutes: j + k + l = 1/12.
3. Machine J does one job in 20 minutes, or j = 1/20.
4. The number of jobs completed by machine J is \(j * t = \frac{1}{20} * t = \frac{t}{20}\) and the number of jobs completed by machines K and L working together and with no other machines is \((k + l) * t = (\frac{1}{12} - j) * t = \frac{1}{30} * t = \frac{t}{30}\).
5. The ratio between the two numbers is \(\frac{\frac{t}{20}}{\frac{t}{30}} = \frac{3}{2}\).
6. Out of all the answer choices, only the pair 63 and 42 have this ratio.
7. Our answer will be: The number of jobs completed by machine J - 63 and The number of jobs completed by machines K and L working together and with no other machines - 42.
2. All three machines do one job for 12 minutes: j + k + l = 1/12.
3. Machine J does one job in 20 minutes, or j = 1/20.
4. The number of jobs completed by machine J is \(j * t = \frac{1}{20} * t = \frac{t}{20}\) and the number of jobs completed by machines K and L working together and with no other machines is \((k + l) * t = (\frac{1}{12} - j) * t = \frac{1}{30} * t = \frac{t}{30}\).
5. The ratio between the two numbers is \(\frac{\frac{t}{20}}{\frac{t}{30}} = \frac{3}{2}\).
6. Out of all the answer choices, only the pair 63 and 42 have this ratio.
7. Our answer will be: The number of jobs completed by machine J - 63 and The number of jobs completed by machines K and L working together and with no other machines - 42.
General Discussion
14 Jan 2025, 22:46
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Rate of Work of Machine J = 1/20.
Rate of Work of Machines K+L = 1/12-1/20=1/30.
Now both machines work for the same time.
Hence We need to assume the Work done by J alone, then reverse calculate the time taken, then find out if corresponding work done for K+L is present in the options or not.
Eg:
Checking for 24(for J)
For J to have done 24 units of work, Total time was 24(1/20)=24*20
Therefore for K+L total work done would be = 24*20*1/30 = 16 (Not available)
Check for 63 (for J)
Total Time allocated was 63/(1/20)=63*20
Work done by K+L = 63*20/30= 42
Rate of Work of Machines K+L = 1/12-1/20=1/30.
Now both machines work for the same time.
Hence We need to assume the Work done by J alone, then reverse calculate the time taken, then find out if corresponding work done for K+L is present in the options or not.
Eg:
Checking for 24(for J)
For J to have done 24 units of work, Total time was 24(1/20)=24*20
Therefore for K+L total work done would be = 24*20*1/30 = 16 (Not available)
Check for 63 (for J)
Total Time allocated was 63/(1/20)=63*20
Work done by K+L = 63*20/30= 42
