A small pool filled only with water will require

[christy.p.lampe]

Hi my question in reference to Question Bank problem set for Manhattan GMAT: Set FDP #11 which reads,

"A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? "

I mimicked my solving for the above problem based upon a similar problem I had done in the FDP strategy guide in chapter 3 page 51 #5 which reads:

" a bowl is half full of water. Four cups of water are added to the bowl filling the bowl to 70% of its capacity. How many cups of water are now in the bowl?"


The solution to the strategy guide problem explains that you can solve for the total capacity of the bowl by use the percent change formula: (20/100)=(4/x) where x is equal to 20 and represents total capacity of the bowl.


Using that same logic, I solved the question bank problem above with 30/100=300/x to get x= 1000 ml (the total capacity) but this is incorrect.

How are these problems different?

[RonPurewal]

The first problem says that the amount of water in the pool is increased by 30 percent.

This percentage is relative to the original amount of water in the pool, NOT to the pool's total capacity.

If this amount were 30% of the pool's capacity, then it would represent a change from 50% full to 80% full. That would actually mean an increase of (80 - 50)/50 = 0.6 = 60%.

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In the second problem, the bowl starts half full (= 50% of capacity), and ends 70% full (= 70% of capacity). Those are all percentages of the bowl's entire capacity, not percentages of the amount of water in the bowl. So, that's a difference of 70% - 50% = 20% of the actual capacity of the bowl.