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21 Sep 2019, 15:57
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Difficulty:
65%
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Question Stats:
57% (02:02) correct
43%
(02:29)
wrong
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In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period?
(1) n = 3m
(2) 2m + 3n = 55
DS01451.01
(1) n = 3m
(2) 2m + 3n = 55
DS01451.01
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21 Sep 2019, 16:57
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from the given, we can deduce that each large machine dis 4 loads, and each small machine did 6 loads during the two hours.
so the question is what is the value of \(4m + 6n = ??\)
from statement (1), the ratio between the large and small machines are given, but this can't provide the exact numerical --> insufficient
from statement (2), if \(2m + 3n = 55\), then \(4m + 6n = 110\) --> sufficient
so the question is what is the value of \(4m + 6n = ??\)
from statement (1), the ratio between the large and small machines are given, but this can't provide the exact numerical --> insufficient
from statement (2), if \(2m + 3n = 55\), then \(4m + 6n = 110\) --> sufficient
26 Jul 2020, 09:08
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official solution
During the two-hour period each large washer does four loads (the number of 30-minute periods in two hours is four) and each small washer does six loads (the number of 20-minute periods in two hours is six). Therefore, the total number of loads done during the two-hour period by m large washers and n small washers is 4m + 6n.
If m = 1 and n = 3, then n = 3m and the total number of loads of laundry done in the two-hour period is 4(1) + 6(3) = 22. However, if m = 2 and n = 6, then n = 3m and the total number of loads of laundry done in the two-hour period is 4(2) + 6(6) = 44; NOT sufficient.
Since 2m + 3n = 55, it follows that 4m + 6n = 110. Therefore, by the remarks above, the total number of loads done during the two-hour period is 110; SUFFICIENT.
During the two-hour period each large washer does four loads (the number of 30-minute periods in two hours is four) and each small washer does six loads (the number of 20-minute periods in two hours is six). Therefore, the total number of loads done during the two-hour period by m large washers and n small washers is 4m + 6n.
If m = 1 and n = 3, then n = 3m and the total number of loads of laundry done in the two-hour period is 4(1) + 6(3) = 22. However, if m = 2 and n = 6, then n = 3m and the total number of loads of laundry done in the two-hour period is 4(2) + 6(6) = 44; NOT sufficient.
Since 2m + 3n = 55, it follows that 4m + 6n = 110. Therefore, by the remarks above, the total number of loads done during the two-hour period is 110; SUFFICIENT.
