prep 1

The bigger jar is the one which gets filled the least.

So, the jar filled to 1/4th is bigger than the jar filled to 1/3rd. Pour the liquid from the jar filled to 1/3rd into 1/4th which will bring it to 1/2 its capacity.

Answer is C.

The way I looked at this one is "A four gallon jar contains one gallon of water, and a three gallon jar holds one gallon of water. What faction of the four gallon jar is filled if I fill it with the contents of the three gallon jar?"

Four gallon jar is currently 1/4 full
Three gallon jar is currently 1/3 full

Add one gallon to the four gallon jar, and it becomes 2/4 full, which reduces to 1/2.

IMO: This is less mathematical and possibly "lame" way to approach the problem, but it got the job done with this question. Not so sure about more complicated problems though.

Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and the other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?

a)1/7
b)2/7
c)1/2
d)7/12
e)2/3

If pouring X liters into the larger jar makes it 1/4 full, then doubling the X liters (by adding the water from the smaller jar) will make the larger jar 2*(1/4) = 1/2 full.

The correct answer is C.

It doesn't matter how full the smaller jar is (1/3). All that matters is that it is the same amount of water as in the big jar ie. 1/4. So if you add another 1/4 to 1/4, you get 1/2.