BTGmoderatorDC wrote:Every object in a box is either a sphere or a cube, and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and 5 green objects in the box.
(2) There are two red spheres in the box.

OA E

Source: Official Guide

Target question: How many objects are in the box?

Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green.
We can solve this using the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions)..
Here, we have a population of objects, and the two characteristics are:
- sphere or cube
- red or green

So, we can set up our matrix as follows:


From here, I'll jump straight to . . .

Statements 1 and 2 COMBINED
When we combine the statements, we get the following matrix:


There are several scenarios that satisfy BOTH statements. Here are two:
Case a:

In this case, the total number of objects = 3 + 3 + 2 + 2 = 10
So, the answer to the target question is there are 10 objects in the box

Case b:

In this case, the total number of objects = 5 + 1 + 2 + 4 = 12
So, the answer to the target question is there are 12 objects in the box

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video: https://www.youtube.com/watch?v=jK-tiBrrf04
Here's a practice question too: https://www.youtube.com/watch?v=DsbPUSH_Wu4