At a certain company, 30 percent of the employees live in City R. If 2

Given: 30 percent of the employees live in City R. 25 percent of the company’s employees live in apartments in City R
One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of employees, and the two characteristics are:
- lives in City R or does not live in City R
- lives in apartment or does not live in apartment

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

We can set up our diagram as follows:

NOTE: I'm letting x = the total number of employees at the company

30 percent of the employees live in City R
If 30% live in City R, then 70% do NOT live in City R.
So, 0.3x = the NUMBER of employees who live in City R
And 0.7x = the NUMBER of employees who DON'T live in City R


25 percent of the company’s employees live in apartments in City R
So, 0.25x = the NUMBER of employees who live in apartments AND live in City R



NOTE: Since the two boxes in the top row must add to 0.3x, the missing box must be 0.05x



Target question: What is the number of the employees who live in apartments AND live in City R?
In other words, What is the value of 0.25x?

Statement 1: Of the employees who live in City R, 6 do not live in apartments.
The top right box (0.05x) represents the NUMBER of employees who live in the city R but do not live in apartments.
So we can write: 0.05x = 6
Solve: x = 6/0.05 = 120
If x = 120, then 0.25x = 30, which means 30 employees live in apartments AND live in City R
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Of the employees, 84 do not live in City R.
Since 0.7x = the NUMBER of employees who DON'T live in City R, we can write: 0.7x = 84
Solve: x = 84/0.7 = 120
If x = 120, then 0.25x = 30, which means 30 employees live in apartments AND live in City R
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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:



EXTRA PRACTICE QUESTION