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In a print shop, 36 identical printers working together can print a batch of flyers in 3 hours. Initially, 24 printers started printing, and after 2.5 hours, 48 identical reserve printers joined them. Will it take more than 1.5 hours for all the printers together to finish printing the batch?
(1) The rate of a reserve printer is 1/4th of the rate of an original printer.
(2) The rate of a reserve printer is lower than the rate of an original printer.
(1) The rate of a reserve printer is 1/4th of the rate of an original printer.
(2) The rate of a reserve printer is lower than the rate of an original printer.
08 May 2025, 01:45
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Official Solution:
In a print shop, 36 identical printers working together can print a batch of flyers in 3 hours. Initially, 24 printers started printing, and after 2.5 hours, 48 identical reserve printers joined them. Will it take more than 1.5 hours for all the printers together to finish printing the batch?
Assuming each printer completes 1 unit of work in 1 hour, the total work would be 36 * 3 = 108 units. In 2.5 hours, 24 printers would complete 24 * 2.5 = 60 units of work. In the next 1.5 hours, they would complete 24 * 1.5 = 36 units of work, leaving 108 - 60 - 36 = 12 units. So essentially, the question boils down to whether 48 reserve printers can complete these remaining 12 units of work in 1.5 hours.
(1) The rate of a reserve printer is 1/4th of the rate of an original printer.
From the stem, we know the rate of an original printer, so from this statement we can get the rate of a reserve printer, which was the only missing piece. Now, we know everything, and there is no need to calculate anything for this statement. From the stem, we know the rate and number of original printers involved, and the size of the work to be done. From this statement, we know the rate of the reserve printers. We also know all the relevant time values given in the question. Therefore, we can surely answer any question about this setup. Sufficient.
(2) The rate of an original printer is higher than the rate of a reserve printer.
48 original printers would complete 48 * 1.5 = 72 units of work in 1.5 hours, which is more than the 12 units remaining. We know that reserve printers would complete less, but we don't know by how much. Depending on how slow they are, the group could either finish the remaining work in less than or more than 1.5 hours. Thus, this statement alone is not sufficient.
Answer: A
In a print shop, 36 identical printers working together can print a batch of flyers in 3 hours. Initially, 24 printers started printing, and after 2.5 hours, 48 identical reserve printers joined them. Will it take more than 1.5 hours for all the printers together to finish printing the batch?
Assuming each printer completes 1 unit of work in 1 hour, the total work would be 36 * 3 = 108 units. In 2.5 hours, 24 printers would complete 24 * 2.5 = 60 units of work. In the next 1.5 hours, they would complete 24 * 1.5 = 36 units of work, leaving 108 - 60 - 36 = 12 units. So essentially, the question boils down to whether 48 reserve printers can complete these remaining 12 units of work in 1.5 hours.
(1) The rate of a reserve printer is 1/4th of the rate of an original printer.
From the stem, we know the rate of an original printer, so from this statement we can get the rate of a reserve printer, which was the only missing piece. Now, we know everything, and there is no need to calculate anything for this statement. From the stem, we know the rate and number of original printers involved, and the size of the work to be done. From this statement, we know the rate of the reserve printers. We also know all the relevant time values given in the question. Therefore, we can surely answer any question about this setup. Sufficient.
(2) The rate of an original printer is higher than the rate of a reserve printer.
48 original printers would complete 48 * 1.5 = 72 units of work in 1.5 hours, which is more than the 12 units remaining. We know that reserve printers would complete less, but we don't know by how much. Depending on how slow they are, the group could either finish the remaining work in less than or more than 1.5 hours. Thus, this statement alone is not sufficient.
Answer: A
General Discussion
28 Apr 2025, 09:21
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Given: 36 printers can do a batch in 3hrs
Required : Time taken by (48+24 =72 printers ) <1.5 hr?
Case-1: Rate of 48 printers < rate of 36 printer, which means the time taken by 48 reserve printers to print a batch is more than 3 hours. And combined with 24 printers the time will be more than 1.5hrs since, 72 printers at original rate can print a batch in exactly in 1.5hrs. If the rate of either 24 printers or 48 printers is decreased than the time will exceed 1.5hrs.
Case-2: Rate of reserve printer (48nos) < rate of original printer (36). Same explanation as in case-1.
Hence both options can able to answer the question in a definite manner. So option D
Required : Time taken by (48+24 =72 printers ) <1.5 hr?
Case-1: Rate of 48 printers < rate of 36 printer, which means the time taken by 48 reserve printers to print a batch is more than 3 hours. And combined with 24 printers the time will be more than 1.5hrs since, 72 printers at original rate can print a batch in exactly in 1.5hrs. If the rate of either 24 printers or 48 printers is decreased than the time will exceed 1.5hrs.
Case-2: Rate of reserve printer (48nos) < rate of original printer (36). Same explanation as in case-1.
Hence both options can able to answer the question in a definite manner. So option D
