Question

Water is pumped into a partially filled tank at a constant rate through an inlet pipe. At the same time, water is pumped out of the tank at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the tank increasing?
(1) The amount of water initially in the tank is 200 gallons.
(2) Water is pumped into the tank at a rate of 10 gallons per minute and out of the tank at a rate of 10 gallons every 2~ minutes.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Arithmetic Work

Problem If both the rate of the water being pumped in to the tank and the rate of the water being pumped out of the tank are known, then the rate at which the total amount of water in the tank is changing can be determined, but not if only one of these quantities is known.

(1) This only gives the amount of water in the tank initially; NOT sufficient.

(2)This information provides both the needed rates. Since the water is being pumped out of the tank at the rate of 10 gallons every $2\frac{1}{2}$ minutes, that is, 4 gallons every minute,and since 10 gallons are pumped into the tank every minute, the rate at which the water is increasing in the tank is $10-4=6$ gallons per minute; SUFFICIENT.

The correct answer is B; statement 2 alone is sufficient.