GMAT Math : Volume trap

Let’s start with a GMAT Data sufficiency example:

Bob is filling a cylinder with solid pellets. The cylinders radius is 10 cm and its height is 100 cm. How many maximum number of pellets fit into the cylinder?

  1. The volume of the pellet is 60π cm2
  2. The pellet is a cone with base radius 3 cm and height 20 cm

Readers are encouraged to take some time to tackle this problem 🙂

It might be tempting to use the following equation:

# of pellets that fit in = volume of cylinder/volume of pellet

The formula assumes that the WHOLE volume of the cylinder is filled with pellets.

However, solid pellets unlike fluids like air or water may not be able to fill the cylinder fully.

Here’s an example:

Notice, the little bit of room between each pellets since they do not slot perfectly with each other. Without knowing the shape and dimensions of the pellets its impossible to determine the # of pellets that can fit in.

So, option (1) by itself is not sufficient.

Option (2) on the other hand gives us the shape AND the dimensions of the shape.

Now, we may have to determine the exact orientation of the cones (trial and error in slotting in the cones) to maximize the number of cones that fit in and this would take a lot of time and maybe even some computer modelling.

The more important point is that it is theoretically achievable with the information given.

The golden trick of data sufficiency questions is that we do not have to determine the actual ‘answer’ but just be able to claim if the answer is achievable or not.

We go with option (B)