Question on doing quick math

JDesai01 wrote:These easy questions always seem to trip me up on time:

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82% of the total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

Very easy getting to 0.82t=138, but does anyone have suggestions on how to quickly do the math for 138/0.82?

The answer choices are usually close enough to each other where you need to go through the long multiplication.

Any tips would be greatly appreciated. Thanks

Notice that the question asks 'approximately', not 'exactly', which means we can get away with doing some estimation or rounding here. It would helpful to see the answer choices- these would give us some idea of how much latitude we have when rounding. What I notice here-

138 bn corresponds to 82%
13.8 bn corresponds to 8.2%
14 bn corresponds to something close to 8%

So if we are at 82%, we are 18% under capacity, or 8% + 8% + 2% under capacity, which is close to 14 + 14 + 14/4 billion gallons under. Thus the total capacity should be roughly 138 + 31.5, or approximately 169.5. The actual answer is 168.3 to one decimal place, so this estimate is quite good, but wouldn't be good enough if the answers were very close together. How far apart were the answer choices here?