GMAT PREP I RATE

pkw209 wrote:Hi all,

Couldn't figure this one out. Thought the answer was C but it is E. FYI, I took this directly from Zuleron's list of 198 questions.
Thanks!

96) X and Y work at constant rates, how many more hours does it take machine y, alone, to fill an order of a certain size than machine X alone.

a. X and Y together fill order in 2�3 the time that X alone does
b. Y alone does it in twice the time as X alone does

Again, I would use reasoning over algebra, although you could also refer to the combined work formula here.

(1) X and Y together fill order in 2/3 the time that X alone does

So, when X gets Y's assistance, the time is cut by 1/3. So, for one job, X does two out of three parts, while Y does one out of three parts. This means that X is twice as fast as Y (or that Y is twice as slow). This is clearly insufficient.

(2) provides the exact same info.

Choose E.

__________

Algebra for (1):

T(xy) = Tx*Ty/(Tx + Ty) [combined work formula]

(1) tells you that T(xy) = 2/3*Tx...sub in on left hand side:

2/3*Tx = Tx*Ty/(Tx + Ty)

Tx = Ty/2

(in other words X must be twice as fast as Y).

Remember that rate and time are always inversely related.

Thanks. I see why the answer is E after re-doing the algebra although I now think my algebra is incorrect.

1) I translated into 1/x + 1/y = 3/2 x

2) I translated into 1/y = 1/2x

therefore, I can find ratio of x to y but still can't find values for x or y.

however, where did I go wrong with my algebra? As you can see, I'm using the other version of the combined work formula although it should come out to the same...

pkw209 wrote:Thanks. I see why the answer is E after re-doing the algebra although I now think my algebra is incorrect.

1) I translated into 1/x + 1/y = 3/2 x

2) I translated into 1/y = 1/2x

therefore, I can find ratio of x to y but still can't find values for x or y.

however, where did I go wrong with my algebra? As you can see, I'm using the other version of the combined work formula although it should come out to the same...

1/x + 1/y = 3/2x

2/2x + 1/y = 3/2x

1/y = 3/2x - 2/2x

1/y = 1/2x