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quantitative review green book, problem solving question 173

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by beatthegmat2 » Wed Jan 18, 2012 10:53 am
Running at their respective 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 of a widget in 3 days. How many days would it take machine x alone to produce 2 w widgets?

A 4
B 6
C 8
D 10
E 12

I know there has to be a shortcut rather than doing all of that math, has anyone seen it in this problem?
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by pemdas » Wed Jan 18, 2012 11:27 am
machine x time relative to machine y time -> x=y+2, their speeds @ x will be 1/x and 1/y OR 1/(y+2) and 1/y

two machines together produce implies 1/(y+2) + 1/y = 5/4 : 3 and solve for y to find x
1/(y+2) + 1/y = 5/12, 5y(y+2)=12y+12(y+2), 5y^2+10y-24y-24=0 and 5y^2-14y-24=0

y(1,2)=(14+-sqroot(196+20*24))/10=(14+-sqroot(676)/10 count only +ve root(s)
y=14+26/10=4 and x=4+2=6

Q.: How many days would it take machine x alone to produce 2 w widgets? one widget is produced in 6 days, 2 widgets are produced in 12 days

e
beatthegmat2 wrote:Running at their respective 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 of a widget in 3 days. How many days would it take machine x alone to produce 2 w widgets?

A 4
B 6
C 8
D 10
E 12

I know there has to be a shortcut rather than doing all of that math, has anyone seen it in this problem?
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by LalaB » Wed Jan 18, 2012 11:40 am
if x and y need 3 days to produce 5/4w, then they need 3*4/5days to produce 1w.

t(t+2)/(t+2+t)=12/5

t=4

x needs 6 days (4+2) to produce w, and 12 days to produce 2w
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by MakeUrTimeCount » Wed Jan 18, 2012 12:18 pm
For this , I suggest the reverse approach.

We know that, if
x takes 'M' days to complete make w widgets and
y will take 'N' days to make w widgets
So,
N = M-2 -------------------------------(i)

x and y takes 3 days for 5/4w widgets so 1 day's work of x and y collectively= 5w/12
w/M + w/N = 5w/12
=> 1/M + 1/N = 5/12 --------------(ii)

Because x makes w widgets in 'M' days, then he will make 2w widget in '2M' days.

Now use the options (which is equal to 2M) and equation (i) and check by putting values in equation(ii):
A. 4 => M = 2, N = 0 Insufficient
B. 6 => M = 3, N = 4 Insufficient
C. 8 => M = 4, N = 2 Insufficient
D. 10 => M = 5, N = 3 Insufficient
E. 12 => M = 6, N = 4 Sufficient

Ans: E
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