Machine \(A\) produces pencils at a constant rate of \(9000\) pencils per hour, and machine \(B\) produces pencils at a constant rate of \(7000\) pencils per hour. If the two machines together must produce \(100,000\) pencils and if each machine can operate for at most \(8\) hours, what is the least amount of time, in hours, that machine \(B\) must operate?
A. \(4\)
B. \(4 \frac23\)
C. \(5\frac13\)
D. \(6\)
E. \(6 \frac14\)
Answer: A
Source: GMAT Paper Tests
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Machine \(A\) produces pencils at a constant rate of \(9000\) pencils per hour, and machine \(B\) produces pencils at
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To MINIMIZE machine B's operating time, we must MAXIMIZE the time machine A's operating time.Gmat_mission wrote: ↑Sun Dec 12, 2021 1:42 amMachine \(A\) produces pencils at a constant rate of \(9000\) pencils per hour, and machine \(B\) produces pencils at a constant rate of \(7000\) pencils per hour. If the two machines together must produce \(100,000\) pencils and if each machine can operate for at most \(8\) hours, what is the least amount of time, in hours, that machine \(B\) must operate?
A. \(4\)
B. \(4 \frac23\)
C. \(5\frac13\)
D. \(6\)
E. \(6 \frac14\)
Answer: A
Source: GMAT Paper Tests
So, let machine A operate for the full 8 hours.
In 8 hours, machine A produces 72,000 pencils [8 hours x 9,000 pencils/hour =72,000 pencils]
So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000
Time = output/rate
So, operating time = 28,000/7000 = 4 hours
Answer: A
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