题目信息
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?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Algebra Simultaneous equations
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.
The correct answer is B;statement 2 alone is 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.
The correct answer is B;statement 2 alone is sufficient.
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