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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?
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
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28 Apr 2020, 10:12
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parkhydel wrote:
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
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:
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
[#permalink]
28 Apr 2020, 06:11
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parkhydel wrote:
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
PS24210.02
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
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
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28 Apr 2020, 06:28
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Expert Reply
parkhydel wrote:
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
PS24210.02
The easiest way to approach 2 sets questions is the Double Matrix Method.
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
[#permalink]
01 May 2020, 03:13
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Kudos
Expert Reply
parkhydel wrote:
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
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.
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
[#permalink]
15 May 2021, 03:14
Expert Reply
parkhydel wrote:
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
PS24210.02
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Answer: Option E
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Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
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14 Jul 2021, 10:13
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?
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
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14 Jul 2021, 10:44
LamboWalker wrote:
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
Re: According to a survey of 200 people, 60 enjoy skiing and 80 enjoy skat
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07 Aug 2021, 02:20
parkhydel wrote:
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?
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