Moving Volume Between Containers in GMAT Geometry

This question is about volume; while volume is a relatively rare concept on the GMAT, you sometimes see a harder question in which the volume in one container will be “poured” into another.

Below, we have a certain volume in a cylinder. Volume of a cylinder = pi*r^2*h (area of the circle/base x the height of the tube). Then we pour that volume into a rectangular prism.

Let’s look at the specific wording:

A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

This is a “Value” DS question, so sufficiency will be achieved if a statement allows for one value and one value only.

To know what percent more solution would be needed to fill the aquarium, we need to know HOW FULL it currently is. So we need two pieces of info:

-the amount of the original volume (pi*r^2*h)
-the total volume of the prism (Volume = lwh)

To know how full it currently is, is essentially that ratio of (pi*r^2*h)/lwh.

If we ignore pi, we essentially need to understand the ratio between the radius and the length and width, and the ratio of the heights.

Let’s look at the statements:

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

This gives us a relationship between the width and length to the diameter, but not quite enough info. It basically says that:
diameter = 2(w^2 + l^2), once we simplify it down. This is great, since we know radius is half the diameter, but we don’t know anything about the heights.

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

This gives us the info we need about the heights! They are equal! And also, the diameter is equal to the width of the aquarium. We have the relationships we need to solve.

The correct answer is (C).

Takeaway: I would not recommend you actually attempt to solve a question like this on the exam. It is definitely going to take way more than 2 minutes, and I think it’s a 700+ level “time-waster.” If you can’t “logic” your way through it, I think making your best guess and moving on is the way to go.