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01 Jul 2023, 09:32
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A
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A bank has 2 paper shedding machines, one large and one small, to shred sheets of secure waste paper, all of which are the same size. The large machine shreds sheets at a constant rate that is 5 times the constant rate of the small machine. How many minutes would it take the small machine, working alone at its constant shredding rate, to shred n sheets of the paper?
(1) Working together at their individual constant rates, the machines could shred n sheets of the paper in 40 minutes.
(2) n = 1,200
(1) Working together at their individual constant rates, the machines could shred n sheets of the paper in 40 minutes.
(2) n = 1,200
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08 Jul 2023, 15:10
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houston1980
If the rate of the small machine is r, then the rate of the large machine is 5r.
rate × time = work
We need to answer the question:
time_S = work/rate = n/r = ?
Statement One Alone:
=> Working together at their individual constant rates, the machines could shred n sheets of paper in 40 minutes.
The combined rate of the two machines is r + 5r = 6r.
rate × time = work
6r × 40 = n
n/r = 240 minutes
Statement one is sufficient. Eliminate answer choices B, C, and E.
Statement Two Alone:
=> n = 1,200
1,200/r = ?
Clearly, we don’t have enough information to get a unique value. Statement two is not sufficient.
Answer: A
01 Jul 2023, 10:24
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houston1980
The large machine shreds sheets at a constant rate that is 5 times the constant rate of the small machine.
Inference: As the rate of the large machine is 5 times the rate of the small machine the time required by the large machine will be \(\frac{1}{5}\)th the time taken by the small machine to do the same amount of work .
- Time taken by the small machine to shred n sheets of the paper= 5t
- Time taken by the large machine to shred n sheets of the paper= t
Question: 5t?
Statement 1
(1) Working together at their individual constant rates, the machines could shred n sheets of the paper in 40 minutes.
If the time taken by machine A to complete a given amount of work = \(t_1\) and the time taken by machine B to complete the same amount of work = \(t_2\), the time taken to complete the work when both the machine work together simultaneously and independently is given by \(\frac{t_1*t_2}{t_1+t_2}\).
Using the above concept -
Time taken by the small machine and the large machine to shred n sheets of the paper = 40 mins
\(\frac{5t*t}{5t+t}\) = 40
\(\frac{5t^2}{6t}\) = 40
\(\frac{5t}{6}\) = 40
As we have a single variable we can find the value of t and the value of 5t.
The statement alone is sufficient. We can eliminate B, C, and E.
Statement 2
(2) n = 1,200
The statement alone is not sufficient to find the time required by any of the machines.
Eliminate D.
Option A
