Figure:

Often drawing a figure will help to understand the question better and will help with the solution.

First solution:

Find the total capacity of the reservoirs by making a proportion:
138 billion gallons are 82% of total capacity;
t billion gallons are 100% of total capacity.

t = 138* = = 175 billion gallons. So, prior to the rainstorm the reservoirs were short by approximately 175 – 124 = 51 billion gallons. The closest approximate answer is 44 billion gallons.

Second solution:

The total capacity is 20% more than the amount of water after the rainstorm (because or 20%). The total capacity is 138*1.2=166 and prior to the rainstorm the reservoirs were short by approximately 166 – 124 = 42 billion gallons. The closest approximate answer is 44 billion gallons.

Strategy:

Approximate calculation will help you save time. At the same time, you have to be careful and not go too far from original numbers. Moreover, if you see that your approximate answer is also close to other choice(s), it would be better to revise your calculation, increasing accuracy.

Advanced Strategy (700+):

Through approximate calculation you can also aproximate the deviation from the original numbers to help you in turn arrive to an almost exact answer. For example, 138/82 ≈ 140/82 (1% greater) ≈ 140/80 (~ (1% + 2%) greater) ≈ 175 (~ 3 % greater) ≈ 170
the precise answer is 168. So, 170 is much better approximation than 175. How did we get 1% at the first step? 1% of 138 is ~ 1.4. We increase 138 by 2 or ~ 1%. The same approach at the second step: 82-80 = 2 or ~ 2% of 82. In other words, we decrease the denominator by 2 or 2% and it increases the expression by 2%.
This advanced approach seems to be complicated but you can master it.

Useful formulas:

Proportion, percentage.