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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Work problem using smart number
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HPengineer
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https://www.beatthegmat.com/how-many-day ... 11577.htmlHPengineer 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!!
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
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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Another approach would be to plug in the answer choices, which represent the time for X to produce 2w widgets.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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