Data Sufficiency

Right now, a barrel of water is exactly 40% full of water. What is the volume of the barrel?

(1) If the water in the barrel right now were increased by 25%, then the barrel would be exactly half full.

(2) If a volume of water equal to half of what is in the barrel right now were added to the barrel, the empty space left in the barrel then would equal 75% of the volume of the water now.

OA: E

Since every value in the problem is either a fraction or a percentage -- and no actual volumes are given -- the capacity of the barrel can be any value.
Thus, the two statements combines are INSUFFICIENT.

The correct answer is E.

gmattoend wrote: Right now, a barrel of water is exactly 40% full of water.

(2) If a volume of water equal to half of what is in the barrel right now were added to the barrel, the empty space left in the barrel then would equal 75% of the volume of the water now.

The phrase in red is ambiguous and would not appear in an official Quant problem.
This phrase seems to refer to the volume of water currently in the barrel.
As a result, Statement 2 makes no sense.
Consider the following case:
Capacity of the barrel = 100 liters.
Current volume of water = 40% of the barrel = 40 liters.
After the volume of water is increased by 1/2, the new volume of water = 40 liters + 20 liters = 60 liters.
Resulting empty space = (capacity of the barrel) - (new volume of water) = 100-60 = 40 liters.
The resulting empty space (40 liters) is not 75% of the current volume of water (40 liters).
Feel free to ignore this problem.