Data Sufficiency

Two water tanks, X and Y, were drained simultaneously. If X contained 30 more gallons of water than Y, and both tanks became empty at the same time, how long did it take the tanks to empty?

(1) For every gallon drained from tank Y, 2 gallons were drained from tank X.
(2) Tank Y was drained at a constant rate of 20 gallons per hour

Ans C

[email protected] wrote:Two water tanks, X and Y, were drained simultaneously. If X contained 30 more gallons of water than Y, and both tanks became empty at the same time, how long did it take the tanks to empty?

(1) For every gallon drained from tank Y, 2 gallons were drained from tank X.
(2) Tank Y was drained at a constant rate of 20 gallons per hour

Ans C

Given : Capacity X = Capacity Y + 30

Question : Time of Drainage of the tanks = ?

Time of Drainage = Capacity of the Tank / Rate of Drainage
Therefore, we need to calculate Capacities of Tanks and rate of drainage

Statement 1) For every gallon drained from tank Y, 2 gallons were drained from tank X
Which mean if tank Y drains Y gallon then tank X drains 2Y gallons
but Since the both empty the same time therefore,
that mean if tank Y drains Y gallon then tank X drains X gallons
i.e. X = 2Y
But since X = Y + 30
therefore Y + 30 = 2Y
i.e. Y = 30 and X = 60
This only gives us the capacities and not the rate of drain. Therefore Time of Drainage can't be calculated
INSUFFICIENT

Statement 2) Tank Y was drained at a constant rate of 20 gallons per hour
But capacities of Tanks are unknown therefore
INSUFFICIENT

Combining the Two statements
Capacities are known from Statement 1
Rate of Drainage is known from Statement 2, therefore
SUFFICIENT

Answer: Option C

Let the Quantity of water for tank X be Qx and Quantity of water for tank Y be Qy.
From the question we know: Qx=Qy+30
We need to find the time T.
Statement 1: Rx=2Ry (rate of water drainage)since we need to know rate of at least one its insufficient.
Statement 2: Ry=20 gallons/hour. Since we dont know relation between the Rx and Ry, its insufficient.
Both statements together - we can solve: T=Q/R.

[email protected] wrote:Two water tanks, X and Y, were drained simultaneously. If X contained 30 more gallons of water than Y, and both tanks became empty at the same time, how long did it take the tanks to empty?

(1) For every gallon drained from tank Y, 2 gallons were drained from tank X.
(2) Tank Y was drained at a constant rate of 20 gallons per hour

Since X contains 30 more gallons than Y, we get:
X=Y+30.

Statement 1: For every gallon drained from tank Y, 2 gallons were drained from tank X.
Since tank X is drained TWICE AS FAST as tank Y, and both tanks become empty AT THE SAME TIME, tank X must contain TWICE AS MANY GALLONS as tank Y.
Thus, X=2Y.

Since X=Y+30 and X=2Y, we get:
Y+30 = 2Y
30 = Y.

No way to determine how much time is required to empty the two tanks.
INSUFFICIENT.

Statement 2: Tank Y was drained at a constant rate of 20 gallons per hour.
If Y=20 gallons, then the time required to empty each tank = w/r = 20/20 = 1 hour.
If Y=40 gallons, then the time required to empty each tank = w/r = 40/20 = 2 hours.
Since the time can be different values, INSUFFICIENT.

Statements combined:
Statement 1: Y = 30 gallons.
Statement 2: Rate = 20 gallons per hour.
Thus, the time required to empty each tank = w/r = 30/20 = 1.5 hours.
SUFFICIENT.

The correct answer is C.