machines

[dreamv]

Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

1) Machine X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.

[Anurag@Gurome]

Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

1) Machine X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.

Let Machine X takes 'a' hours working alone and machine Y takes 'b' hours working alone to fill a production order. So, we need to find b - a.

(1) Machine X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.
1 hr work of machine X = 1/a and 1 hr work of machine Y = 1/b
1 hr work of machines X and Y, together = 1/a + 1/b = (a + b)/ab
So, time taken by X and Y working together = ab/(a + b)
It is given that ab/(a + b) = 2a/3
3b = 2a + 2b
b = 2a; NOT sufficient.

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.
b = 2a; NOT sufficient.

Combining (1) and (2), we do not get any additional info, as both the statements give the same info; NOT sufficient.

The correct answer is E.

[pemdas]

We denote times for machines X and Y as X and Y, then their respective speeds will be for machine X, 1/X and for machine Y, 1/Y. We need to find the difference in times (Y - X)?

st(1) implies the ratio of speed 1/X to the combined speed (1/X + 1/Y) is set as 2/3.
1/X : (X+Y)/XY = 1/X *XY/(X+Y) = Y/(X+Y) = 2/3 and 2X+2Y=3Y or 2X=Y.
Obviously this is Not Sufficient to find the definite answer for (Y-X) as with 2X-X=X the answer depends on the value of X.

st(2) implies the ratio of speed 1/Y to speed 1/X is set as 2 or Y=2X, which is basically the same condition as in st(1). Not Sufficient

combining st(1&2): nothing new added by combining two statements together, Not Sufficient

e

Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

1) Machine X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.

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Hi experts,
is there a shortcut for Work/Rate Data Sufficiency problems?
I know for triangles there are shortcuts so that you know if a statement is sufficient or not.
Thanks!