Machine X and Y work at their respective constant rates - DS

[Guest]

My date is on Wednesday. I would like to ask if someone can explain the answer.

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

OA is E. I get y=2x from the two statements. Therefore, Machine Y hours will be doube the Machine X hours. So why is the answer E?

Thank you.

[abovethehead]

Let x and y represent the respective rates of X and Y.
We must know the values of both x and y to know "how many more hours". In other words, y = 2x does not tell us how many more hours the job takes Y than X, only that Y takes twice as long. If x = 2, y = 4 and the difference is 2. However, if x = 3, y = 6, and it now takes 3 hours longer.

1) 1/x + 1/y = 1/T
So, T (total time) = xy / (x+y)
Statement 1 tells us that the total time or combined = 2/3 x
So, xy / (x+y) = 2/3 x
Solve and you get y = 2x
INSUFFICIENT - again, it only gives us a relationship

2) translated gives y = 2x

Statements 1 and 2 provide the same information, so either D or E
Since we cannot combine 2 similar equations to solve for 2 variables, the answer is E

[Guest]

Got it. Thank you.

[fangming_li]

"Let x and y represent the respective rates of X and Y.
1) 1/x + 1/y = 1/T
So, T (total time) = xy / (x+y) "


x and y should not be letted as rates of X and Y. It should be
time.

[mschwrtz]

That right. I assume that that was just a slip of the keyboard, abovethehead, since you treated the variables as representing times throughout your explanation.

[sudaif]

thanks for pointing out the m. he had me confused for a second!

[RonPurewal]

glad it helped

[raviteja.pandiri]

But we are having a definite quantity "X"..Right?So I still feel the answer is D.

Because there is no other value/variable affecting the outcome except for the "X".Please clarify if I am going badly wrong somewhere!

[tim]

um, X is not a definite quantity. definite quantities are specific numbers, not variables, not ranges of numbers, not even choices between two numbers. if you get an answer of X, that means you don't know for sure what the answer is since X can mean many things..