Machine A produces pencils at a constant rate of 9000

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Jan 21, 2019 2:05 pm

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Source: GMAT Prep

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 to gather 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 2/3
C. 5 1/3
D. 6
E. 6 1/4

The OA is A

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Source: Beat The GMAT — Problem Solving | Mon Jan 21, 2019 2:05 pm

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by GMATGuruNY » Mon Jan 21, 2019 2:13 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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 to gather 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 2/3
C. 5 1/3
D. 6
E. 6 1/4

To minimize B's time, we must maximize A's time.
Since each machine can work for at most 8 hours, let A's time = 8 hours.
Since A's rate = 9000 pencils per hour, the number of pencils produced by A in 8 hours = rt = 9000*8 = 72,000.
Remaining pencils = 100,000 - 72,000, = 28,000.
Since B's rate = 7000 pencils per hour, the time for B to produce the remaining 28,000 pencils = w/r = 28,000/7000 = 4 hours.

The correct answer is A.

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by Scott@TargetTestPrep » Sun Jan 27, 2019 6:17 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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 to gather 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 2/3
C. 5 1/3
D. 6
E. 6 1/4

If machine B's operational time is to be minimized, we must maximize the time for machine A to operate. Since each machine can operate for at most 8 hours, we can let machine A operate for the full 8 hours. Since the rate of machine A is 9000 pencils per hour, machine A produces 8 x 9000 = 72,000 pencils, and thus 28,000 pencils are left to be produced.

Thus, it will take machine B 28,000/7,000 = 4 hours to produce the remaining pencils.

Answer: A

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