capacity of a tank

[Gurpinder]

When 200 gallons of oil were removed from a tank, the volume of oil left in the tank was 3/7 of the tank's capacity. What was the tank's capacity?
(1) Before the 200 gallons were removed, the volume of oil in the tank was 1/2 of the tank's capacity.
(2) After the 200 gallons were removed, the volume of oil left in the tank was 1,600 gallons less than the tank's capacity.

_____________

x-200=3/7x
Solving this, you get x = 350

What is the relationship of 350 to this question. Is 350 the tank's capacity? Or is it the amount of oil in the tank?
I am so confused!

[GmatKiss]

IMO : D

the equation is,

x-200 = 3/7*volume

[goalevan]

You cannot use one variable to represent both the starting volume and the capacity of the tank, because it is never stated that the tank starts out full.

We have to create another variable for the capacity: t, and keep it separate from the starting volume: x.

x - 200 = (3/7)t, "what is t?"

The above is a single linear equation in two variables, so the introduction of any independent linear equation that relates the variables x and t will allow us to solve.

Statement 1) this statement says that the starting volume (x) was 1/2 of the capacity (t), so x = (1/2)t. Immediately we can see that this is an independent linear equation that will allow us to solve for t, so it is sufficient.

Just to illustrate the calculation, [(1/2)t] - 200 = (3/7)t, so t = 200 * 14 = 2,800 gallons.

Statement 2) this statement says that the volume after 200 is removed is 1,600 gallons less, so x - 200 = t - 1,600.

Since x - 200 = (3/7)t, as given in the question stem, we can substitute to get [(3/7)t] = t - 1,600. Again, this statement is sufficient because it introduces a new linear equation that relates t and x.

The calculation (unnecessary at this point) is (4/7)t = 1,600, so t = 2,800 gallons.

[Gurpinder]

Thanks!

Whats the difference between capacity and volume?

[GmatKiss]

Capacity and Volume mean the same in the context.

It is better to mention tank's capacity instead of tank's volume, and
It is better to mention voulme of oil instead of capacity of oil in the tank.

[Gurpinder]

When 200 gallons of oil were removed from a tank, the volume of oil left in the tank was 3/7 of the tank's capacity.

So the only reason why we can't give the capacity and the volume the same variable in this context is because we don't know whether BEFORE the 200 gallons were removed, whether the tank was full or not.

And by giving them the same variable, the equation would mean that 200 gallons of oil would bring the tank 7/7 to its capacity.

Am I thinking correct?