We can use 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 respondents , and the two characteristics are:
- Used M or didn't use M
- Used N or didn't use N

With the given information, we can set up our matrix as follows:

IMPORTANT: I let x = number of respondents who used BOTH M and N, and I let y = the number who used NEITHER M nor N",
So, from the first sentence, we can write: x + y = 48
ASIDE: I placed a star in the box that the question asks us to find.


Next, since the two boxes on the right column must add to 44, the top-right box must be 44-y


Next, since the two boxes on the top row must add to 39, the top-right box must be 39-x


Since we have two ways to represent the top-right box, we can write: 44-y = 39-x
Add x to both sides to get: 44 - y + x = 39
Subtract 44 from both sides to get: -y + x = -5
Rearrange to get: x - y = -5

We now know that:
x + y = 48
x - y = -5

Add the equations to get: 2x = 43
Solve: x = 21.5

If x = 21.5, then the top-right box = 39 - 21.5 = 17.5

Answer: E


To learn more about the Double Matrix Method, watch this video: