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In a poll, 200 subscribers to Financial Magazine X indicated which of five specific companies they own stock in. The results are shown in the table above. If 15 of the 200 own stock in both IBM and AT&T, how many of those polled own stock in neither company?
(A) 63
(B) 93
(C) 107
(D) 122
(E) 137
Attachment:
2020-04-20_2303.png
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