Data Sufficiency

Hi Everyone,

I wanted to throw this question out there and then ask a follow-up question of my own. Here we go:

Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 liters. If the flow in each hose is independent of the flow in the other hose, how many hours will it take to fill the pool?

(1) Hose X alone would take 28 hours to fill the pool.
(2) Hose Y alone would take 36 hours to fill the pool.

Answer is C, which makes sense because you can take both rates, add them, and figure out the answer, but neither statement alone will get you there.

My question is interpretation of rates. Based on my review, I keep wanting to represent X's rate as 28/50,000 or 7/12,500 and Y's rate as 36/50,000 or 9/12,500.

Combining them I would end up getting 16/12,500 or 4/3,125.

Is this the correct way to interpret these rates? I remember somewhere in the GMAT Prep modules to represent it as TIME/OUTPUT however, when I get there I stumble with how to interpret the final outcome (4/3,125 in this case). When you take it back to 50,000 liters, then you get 64 in the numerator which doesn't make any sense because that would indicate it takes LONGER to get the job done with both hoses.

Obviously, in terms of DS I'm able to figure out that you CAN get the answer, but in terms of PS I want to ensure I arrive at the correct answer value and lay down rates the most concise / logical way while maintaining correct math to combine things.

Thanks for the input!

Ah, good question. And you just have it flipped. You're doing rate = time/distance, when really it's:

Rate = "Distance" / Time

I like thinking of it that way because it's impossible to forget. If you're driving to the test center you'll pass several speed limit signs in "miles (distance) per (divided by) hour (time)", so that should just be ingrained in your mind without your having to memorize anything or hope you memorized it correctly.

So in this case, the rates should be:

Hose X: one pool / 28 hours
Hose Y: one pool / 36 hours

And since the question is asking you about the pool, not the number of gallons, the math is probably easier if you just keep everything in terms of "one pool" and not "50,000 liters".


Hope that helps...

Yup. For whatever reason, I flipped it Time/Output, when I should have been Output/Time.

In that case it would have been 1/28 + 1/36 = 9/252 + 7/252 = 16/252 = 4/63 - Then I would interpret this as 4 Pools in 63 hours which is faster and makes sense.

Thanks for the responses!