Bunuel wrote:
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 44% of respondents did not use M. 39% used N. What percent of respondents used only N?
(A) 21.5%
(B) 20%
(C) 19.5%
(D) 18.5%
(E) 17.5%
Are You Up For the Challenge: 700 Level QuestionsWe 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 = 48ASIDE: 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-yNext, since the two boxes on the top row must add to 39, the top-right box must be
39-xSince we have two ways to represent the top-right box, we can write:
44-y =
39-xAdd 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 = -5We now know that:
x + y = 48x - y = -5Add 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
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:
[you-tube]https://www.youtube.com/watch?v=jK-tiBrrf04[/you-tube
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