Gmat Prep ?? (Machines Working)

[dferm]

Please Help...

Thanks...

[California4jx]

IMO: D

whats OA ? ,

[dferm]

Its D...but can you offer a solution...

Thanks..

[California4jx]

Given: X + Y = 48 mints

convert mints to an hour = 48/60 = 4/5 of an hour

which means when two machines work together, they fill the entire tank in 4/5 of an hour.

Individual rates of each pump are given in statements I and II:

Statement I:

X = 80 mints
= 80/60 = 4/3 of an hour

Rate/hr of X = 1/X = 1 / (4/3) = 3/4
(this is the rate at which pump X fills the tank in an hour, means X fills 3/4 of a tank in 1 hour)

1 hr ---> 3/4 of a tank
in 4/5 of an hour ----> 3/4 * 4/5 = 3/5 of a tank by X

Statement II:

Y = 120 mints
Y = 2 hr
Rate of Y = 1/Y = 1/2
1 hr ------> 1/2 of a tank
in 4/5 of an hr -----> 1/2 * 4/5 = 2/5 of a tank by Y
so 1-2/5 = 3/5 by pump X

So, D is the answer

[lunarpower]

the solution above looks fine, but there is no reason whatsoever to do that much work.

remember, this is DATA SUFFICIENCY, not data solving. you don't have to solve problems once you have ascertained that you CAN solve them.

to this end:

the question prompt tells that the COMBINED RATE for pumps x and y is 1 tank per 48 minutes, or (1/48) tank/min.
notice that this value is the SUM of the individual rates for pump x and pump y; as usual, rates for simultaneous work are additive.

there's no terribly good reason to switch to hours. hours make things easier if you have to solve for actual quantities ... but you don't.

--

REPHRASE THE QUESTION:
because the pumps are working for the same amount of time, the amount of water pumped by each is proportional to the pumping rate. therefore, this question can be answered if you can answer either of the following:
what is the rate for pump x?
what is the rate for pump y?

you can also consider this intuitively, without thinking about the proportion: if you know the rates at which two pumps are pumping, and they're pumping for the same amount of time, then you know the fractions of water that come from each. try to imagine (visually) two pumps that are pumping water in a ratio of, say, 2:1, and this should become clear.

--

statement (1)
rate x = (1/80) tank/min
sufficient

--

statement (2)
rate y = (1/120) tank/min
sufficient

--

note that, even if your rephrase of the question was "what are BOTH rates?" - a perfectly good rephrase - you could still find both rates from either one of the individual statements, via subtraction from the combined rate of 1/48.

[Stuart@KaplanGMAT]

To further Ron's point, data sufficiency questions go much more quickly when you understand the principles on which you're being tested.

Accordingly, you need to be familiar with the commonly tested formulas. One of those is the work formula.

There two variations of the formula - one that's always applicable and one that's for exactly two workers. For this question, either will do.

1/(comb time of all workers) = 1/(time of worker 1) + 1/(time of worker 2) + 1/(time of worker 3) + ...

or

(combined time of workers A&B) = A*B/(A+B),

in which A and B are the individual times.

In both cases, all we need to recognize is that there are 3 variables: combined time, A and B. 3 variable formulas are very common on the GMAT (probability, rate, average, percent and percent change, to name just a few).

In this question, we're given one of the variables (combined time) and asked to find another. We have 2 equations and 3 unknowns, so just about any other piece of (relevant) information will allow us to solve.

(1) concrete value of one of our variables: sufficient.

(2) concrete value of one of our variables: sufficient.

As Ron pointed out, this is the kind of thinking that maximizes efficiency in DS. Just understanding the n linear equations rule (i.e. # of equations vs # of unknowns) will get you a lot of points on test day.[/list]