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Work problem using smart number

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by HPengineer » Fri Oct 15, 2010 12:56 pm
Working this problem i got stuck trying to use a smart number. Any thoughts how to complete it using a smart number for the widgets?


OG quant review #173

Running at their respective constant rates, Machine X takes 2 days longer to produce W widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take to produce 2w widgets?

Thanks in advance!!
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by diebeatsthegmat » Fri Oct 15, 2010 7:03 pm
HPengineer wrote:Working this problem i got stuck trying to use a smart number. Any thoughts how to complete it using a smart number for the widgets?


OG quant review #173

Running at their respective constant rates, Machine X takes 2 days longer to produce W widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take to produce 2w widgets?

Thanks in advance!!
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by bitsho » Sat Oct 16, 2010 2:27 am
Let total widget be 60 i.e. w= 60 . Now X & Y can produce 5/4w i.e. 75 widget in 3 days .


Now To fulfill the required condition in question stem , Y can produce 15 widget per day & X can produce 10 widget per day (i.e. 75 widget in 3 days when they work together)

So Now back to question : How long X will take to produce 2 W widget = 2*60/10 = 12 days
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by GMATGuruNY » Sat Oct 16, 2010 6:52 am
HPengineer wrote:Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A. 4
B. 6
C. 8
D. 10
E. 12
Another approach would be to plug in the answer choices, which represent the time for X to produce 2w widgets.

Answer choice E:
12 days for X to produce 2w widgets means 6 days for X to produce w widgets and 6-2 = 4 days for Y (since X take 2 days longer)
Let w = 12
Rate for X = w/t = 12/6 = 2/day
Rate for Y = w/t = 12/4 = 3/day
Combined rate for X+Y = 2+3 = 5/day
Work completed in 3 days = r*t = 5*3 = 15 widgets
Does 15 = 5/4*w? Yes, because 15 = (5/4)*12. Success!

The correct answer is E.
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