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GMAT Review PS #188 Why didn't Plugging In work?

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by nickknock » Sun Aug 29, 2010 8:07 pm
Greetings all. Here is the problem I have a question on, from the GMAT review 11th edition:

Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 2/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what fraction of its capacity?

A) 3/4
B) 5/6
C) 11/12
D) 7/6
E) 11/6


MY solution was to Plug In.

Capacity of Drum X=12
Capacity of Drum Y=24
Drum X is 6/12 full
Drum Y is 16/24 full

Then I added 6/12+16/24 to get 7/6 which is wrong.

The book explained the right answer, which I understood (they left it in variables) but I don't quite understand why Plugging In did not work, can you guys help me?
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by uwhusky » Sun Aug 29, 2010 8:15 pm
The problem with the approach is that you converted both to 24 when you add them, so they end up with the same capacity.

What you should have done is simply add 6 to to 16/24, which would be 22/24, and deduce down to 11/12, which is the correct answer. But that's probably more confusing than using the suggested method to solve the question.
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by Rahul@gurome » Sun Aug 29, 2010 8:32 pm
Solution:
Let drum X's capacity be V.
So volume of oil in drum X is (1/2)*V.
Drum Y's capacity is 2V.
So volume of oil in drum Y is (2/3)*2V = (4/3)*V.
If all of the oil in drum X is poured into drum Y, volume of oil in drum Y is (1/2)*V + (4/3)*V = (11/6)*V.
Or the fraction of oil in drum Y is [(11/6)*V]/(2V) = 11/12

The correct answer is (C).
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by wdgolden » Mon Aug 30, 2010 4:57 am
If I have a drum that is 1/2 full and then double the size of the drum, the drum will now be 1/4 full. So if I poured X which is half full into Y which is twice as big I would end up with Y being 1/4 full. Now just add the 2/3 that's already in Y.

1/4 + 2/3 = 3/12 + 8/12 = 11/12
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by Brian@VeritasPrep » Mon Aug 30, 2010 1:22 pm
Hey nickknock,

Great responses in this thread thus far, but let me tack on one more - if you want to put your mistake into a broader context, you didn't keep track of units, which is a big mistake to make in any word problems.

Had you put units (gallons or liters, for example) on the numbers you plugged in, you would likely have been fine, as then it would have been pretty clear that the number of gallons in one drum had to be half that of the other, and you wouldn't have gone after that common denominator.

When you're working with problems that have units, make sure that you're always aware of what each number represents. The GMAT is much more conceptual than "calculational" - questions are often designed to try to trick you into simply "crunching numbers" when really what the test wants is to determine how well you make decisions. To make good decisions, make sure that you're always aware of what the numbers mean!
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