According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skating.

BTGModeratorVI wrote: ↑

Mon Jun 22, 2020 6:14 am

According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skating. If the number of people who enjoy neither skiing nor skating is 2 times the number of people who enjoy both skiing and skating, how many people surveyed enjoy neither skiing nor skating?

A. 20
B. 40
C. 50
D. 80
E. 120


Answer: E
Source: Official guide

Aside: I should note that, although we can apply the overlapping sets formula (total = A + B - both + neither) to answer this question, of the formula can be very tricky to use for more advanced overlapping sets questions.
However, the Double Matrix method will work for all overlapping sets questions..

In this question, we have a population of 200 people, and the two characteristics are:
- enjoys skiing or does not enjoy skiing
- enjoys skating or does not enjoy skating
So we can set up our diagram as follows:



60 enjoy skiing and 80 enjoy skating.
If 60 of the 200 people enjoy skiing, then 140 people do not enjoy skiing.
If 80 of the 200 people enjoy skating, then 120 people do not enjoy skating.
Our diagram now looks like this:



The number of people who enjoy neither skiing nor skating is 2 times the number of people who enjoy both skiing and skating
Let x = the number of people who enjoy BOTH skiing and skating
So, 2x = the number of people who enjoy NEITHER skiing NOR skating
Our diagram now looks like this:




At this point, we can see that the two boxes on the RIGHT-HAND column must add to 140. This means 140 - 2x must equal the value in the top right box
Also keep in mind that the sum of the two boxes in the TOP ROW must add to 80. This means 80 - x must equal the value in the top right box


This means we can write: 140 - 2x = 80 - x
When we solve this equation, we get: x = 60


How many people surveyed enjoy neither skiing nor skating?
We already know that 2x = the number of people who enjoy NEITHER skiing NOR skating
Since we now know that x = 60, we can conclude that 2x = 120
So 120 people enjoy NEITHER skiing NOR skating

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

EXTRA PRACTICE QUESTION
https://www.youtube.com/watch?v=DsbPUSH_Wu4

BTGModeratorVI wrote: ↑

Mon Jun 22, 2020 6:14 am

According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skating. If the number of people who enjoy neither skiing nor skating is 2 times the number of people who enjoy both skiing and skating, how many people surveyed enjoy neither skiing nor skating?

A. 20
B. 40
C. 50
D. 80
E. 120


Answer: E
Source: Official guide

Solution:

We can create the equation:

Total = Skiing + Skating - Both + Neither

200 = 60 + 80 - x + 2x

60 = x

So the number of people who enjoy neither is 2(60) = 120.

Answer: E