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

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:


EXTRA PRACTICE QUESTION


More questions to practice with:
EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html
MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html
HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html
KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

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

Asked: 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?

Total = A + B - both + neither

200 = 60 + 80 - x + 2x
x = 200 - 60 - 80 = 60

Number of people surveyed enjoy neither skiing nor skating = 2x = 120

IMO E

The easiest way to approach 2 sets questions is the Double Matrix Method.

Here is the video solution for reference.

We can create the equation:

200 = 60 + 80 - b + 2b

60 = b

Thus, the number of individuals who enjoy neither activity is 2 x 60 = 120.

Answer: E
_________________

SOLUTION:

Its a question that tests on basics of set theory and overlapping sets in particular.

Let "x" be the number of people enjoying BOTH skiing and skating.

Thus, number of people enjoying ONLY Skiing = (60 - x)

Thus, number of people enjoying ONLY Skating=( 80 - x)

Given, the number of people who enjoy NEITHER skiing or skating = 2x

Thus, 200 = (60-x) + x +(80-x) +2x

=> x = 60 and number of people NOT skiing or skating = 2x =2 x 60 =120 (OPTION E)

Hope this helps
Devmitra Sen(Math)

Answer: Option E

Video solution by GMATinsight



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I am failing to understanding the logic behind this question, which made me ponder over the options despite getting the right answer. 80 + 60 i.e. 140 people out of 200 enjoy one sport or the another. How can it be that 120 of them then enjoy neither skating nor skiing when there are just 60 people left?

Out of 140 enjoying both 60 is common between them. Means out of 80 60 enjoys other part of skiing also. (Means skiing is subset of skating) hence all together 80 njoys skating and skiing. Balance 120 does not enjoy anything

Posted from my mobile device

IMO, (E)!

_________________

Let's denote the number of people who enjoy both skiing and skating as "x".
According to the given information, the number of people who enjoy skiing is 60, and the number of people who enjoy skating is 80.

We are also told that the number of people who enjoy neither skiing nor skating is twice the number of people who enjoy both skiing and skating.

Now, let's calculate the number of people who enjoy neither skiing nor skating:

Total number of people surveyed = Total number of people who enjoy skiing + Total number of people who enjoy skating - Number of people who enjoy both skiing and skating + Number of people who enjoy neither skiing nor skating

200 = 60 + 80 - x + 2x

Simplifying the equation, we have:
200 = 140 + x
x = 60

Therefore, the number of people who enjoy neither skiing nor skating is:
Number of people who enjoy neither skiing nor skating = 2 * Number of people who enjoy both skiing and skating = 2 * 60 = 120

Hence, the answer is (E) 120.