dreamv wrote: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.