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MACHINES

by enriqueta26 » Fri Jul 16, 2010 1:03 pm
COULD SOMEBODY PLEASE HELP ME WITH THIS ONE?? (TAKEN FROM QMAT PRACTICE EXAM)

MACHINE A PRODUCES PENCILS AT THE CONSTANT RATE OF 9,000 PENCILS PER HOUR, AND MACHINE B 7,000 PENCILS PER HOUR. 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?
ANSWER: 4

THANK YOU SO MUCH!!
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by kvcpk » Fri Jul 16, 2010 1:16 pm
enriqueta26 wrote:COULD SOMEBODY PLEASE HELP ME WITH THIS ONE?? (TAKEN FROM QMAT PRACTICE EXAM)

MACHINE A PRODUCES PENCILS AT THE CONSTANT RATE OF 9,000 PENCILS PER HOUR, AND MACHINE B 7,000 PENCILS PER HOUR. 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?
ANSWER: 4

THANK YOU SO MUCH!!
A-9000/hr
B-7000/hr

B should be minimum. SO maximise A
So A can produce 8*9000 = 72000
Remaining = 100000-72000 = 28000
Now 28000 can be produced by B in 28000/7000 = 4 hours.

Hope this helps!!
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by enriqueta26 » Fri Jul 16, 2010 2:17 pm
thank you so much, awesome!!
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by Patrick_GMATFix » Fri Jul 16, 2010 6:10 pm
kvcpk's solution is good. In general, to minimize one value, maximize all the others. to maximize one value, minimize all the others.

Here we want to minimize the amount of time B must operate so we must make A work as long as possible. (8hrs is the max). 100,000 pencils need to be produced. If A works for 8 hours (to produce 72,000 pencils), B will only need to work 4hrs to produce the remaining 28,000 pencils. [spoiler]The answer is A (4hrs)[/spoiler]

A more detailed solution and step-by-step video solution can be found at GMATPrep Question 1074. To practice similar questions, set topic='Rates & Work' and difficulty='600-700' in the Drill Generator

Good luck,
-Patrick
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