javzprobz wrote:
Hi everyone,
I do have a specific problem with THE SOLUTION THAT BUNNEL HAS PROVIDED (reveal the first spoiler to see Bunnel's solution and my analysis of it) for this question. Let's first take a look at the question, then I'll explain my problem.
Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?
(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.
Open the spoiler to read my problem with the solution that Bunnel has provided for this question:
I do understand that we need both statements together in order to solve the question since statement 2 just tells us that pump X can fill 30 gallons per minute and we don't how many gallons the job actually is, thus we need statement 2 as well in order to answer the question. Now for the sake of solving a DS question, it's enough to pick answer choice C and move on since we have enough information to answer the question. However, for the sake of discussing the solution that Bunnel has provided, let's take a look at his solution: "Rate*Time=Job time = 1/3 hrs = 20 minutes so (x+y)*20=work now statement 1 gives us: work=900 and statement 2: x=30. So combining statement 1 and 2, we can solve for y since we have (30+y)*20=900, which gives us y=15. Now, my problem is that I solved the problem the way that some of us used to do (also explained in GMATCLUB Math Book, work problem section). I initially set the equation 1/x+1/y=1/20, after reading the question stem (x and y refer to time that pump x and pump y respectively take to do 1 unit of the job). Then I read statement 1 and noticed that it is insufficient, since it just tells us about how much the work is. And read statement 2, which also is insufficient since now we don't how many gallons the work is. But combining statement 1 and 2, I got to this point that pump x can do 1 unit of the job in 30 minutes (900 gallons/30 minutes=30 gallons/1 minute or in other words 1 unit of job/30 minutes). So now I have 1/30 + 1/y = 1/20, and solving this would give me y=60 minutes. Now, why is my answer to how many minutes pump y takes to do the job alone different than Bunnel's to this question? Is there something wrong with my solution or how I solved the question? I would appreciate your help!
Dear
javzprobz,
I'm happy to respond.
You seem to appreciate the ideas of work-rate well, but if you want reinforcement, here's a blog article about it:
http://magoosh.com/gmat/2012/gmat-work-rate-problems/Your problem was that you used the generic variable "y" and were not careful about exactly what it meant. In Bunuel's solution, y is
rate of pump Y, and he correctly finds that the rate is y = 15 gallons/minute. You used the formula to solve for y = 60, but that formula was designed to give you the
time of pump Y. You correctly found that the time is 60 minutes. This is all correct. If Pump Y has a
rate of 15 gallons/ minute, it would fill a 900 gallon pool in a
time of 60 minutes.
I think your takeaways should be:
1) pick more meaningful variables, and be rigorous in defining exactly what you variables mean
2) don't ignore units; you need to be meticulous clear on the units of each and every number in your calculation
3) don't use a formula unless you are 100% clear on exactly what it does and what it is giving you.
As a general rule, relying on formulas is an exceptionally poor way to approach GMAT Quant.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)