In a poll, 200 subscribers to Financial Magazine X indicated which of

Another approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of 200 magazine subscribers and the two characteristics we need to focus on are:
- owns stock in IBM or does not own stocks in IBM
- owns stock in AT&T or does not own stocks in AT&T

So we can set up our diagram as follows:



If 30 of the 200 subscribers own stock in AT&T, then the other 170 subscribers do NOT own stock in AT&T
If 48 of the 200 subscribers own stock in IBM, then the other 152 subscribers do NOT own stock in IBM
When we add this to our diagram we get the following:



At this point, we can complete the rest of our diagram:


Since the bottom-right square represents subscribers who own stock in neither company, the correct answer is E

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.

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

N(IBM) = 48

N(AT&T) = 30

N(IBM)⋂ N(AT&T) = 15

N(IBM) U N(AT&T) = 48+30 - 15 = 63

Number of those polled own stock in neither company = 200-63 =137

Answer: E

Total no. Of people in the poll=200
Using Venn diagram, let no. of people who own only AT&T be a.
Let no. of people who own only IBM be b
Let no. of people who own both AT&T and IBM be c

a+c=30 (AT&T owners from table)
b+c=48 (IBM owners from table)
c=15 (given)
So, solving these we get a=15, b=33, c=15

No.of people who own stock in neither company= 200-(15+33+15) = 137

Posted from my mobile device

Since 30 + 48 - 15 = 63, then the total number of people who own stock in either AT&T or IBM is 63. Since we know there are 200 people in the survey, we know that 200 - 63 = 137 people DO NOT own stock in either company.

Answer: E
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We can set a double set matrix ..

----------------------ATnT------------------------------(ATnT)~-----------



--------IBM-----------15---------------------------------33------------------ IBM =48


--------IBM~----------15--------------------------------137------------------IBM~ = 200-48=152



Total-----------ATnT=30-------------------------(ATnT)~=170-------------Total=200

So ans is E . 137 .

I think this question could have been a little clearer. It threw me off it said "how many own stock in neither company". Are they talking about all the 5 companies or just AT&T and IBM.

SOLUTION:

A NEW OG 2021 QUESTION

Total number of people who own stock in either AT&T or IBM = 30 + 48 - 15

= 63

Total people in the survey= 200

=> People who are NOT in the survey

= 200-63

= 137 (OPTION E)

Hope this helps
Devmitra Sen(Math)

i got confused in what is being asked

how many of those polled own stock in neither company?

which company are these words referring to. ????

shivimonji These words refer to AT&T and IBM.

This is not only a PS question but also a SC question. LOL. Like many others even I was thinking that the question is not clear about which all companies does it mean by neither. Hol' up! The question clearly states the word 'neither' which is referring to IBM, AT&T.
If the question was worded, how many of those polled own stock in 'none' of the companies. We wouldn't be here discussing this.
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Answer: Option E

Video solution by GMATinsight



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Answer: Option E

Video solution by GMATinsight



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Through this Venn diagram we know that the total shareholders of AT&T and IBM combined are 63

The remaining are 200-63=137 and that is our ans

Option E it is

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