Each person who attended a company meeting was either a

100 = 62 + 47 - n(SnE) [where n represents intersection]
=> n(SnE) = 9

=> Number who were only stockholders = n(S) - n(SnE) = 53 percent

Option (B)

I came up with the same answer choice B, but my approach was slightly different!

47% were employees which shall cover those who were only employees and those who were both shareholders and employees.

Thus, the number of attendants who were only shareholders is 100% - 47% = 53%.

Correct me if I'm wrong please!!!

USe venn diagram , matter of 5 secods

Does anyone know how can we solve this question by using the matrix/table ? I'm having difficulties in drawing one.

Thanks for your help!

Here we can use some of our high school set theory =>
N(A U B) = 100=> N(A) = 62 ; N(B)=47
N(intersection) => 62+47-100=9
Only A=>62-9=>53
Smash B

I too used the Double Matrix Approach to solve this.

The Key thing here is to pay attention to - "Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both.".

What this means is there is no one in the Meeting who is neither a Shareholder NOR an employee.

Once this is know the double Matrix can be written quickly. This is already mentioned by one of the users above.

Abhishek009

Abhishek - Could you explain how you arrived at this Venn diagram, please?

OK, still figuring out how I could solve this. I came across a video tut on here to solve questions using double matrix method. In that context, susheel - did you mean NEITHER a stockholder NOR an employee?

GMATPrepNow - Could you help me with the double matrix table as you explained in one of your videos, please?

Hello Blackbox!

Yes, thats correct! I will go and edit the typo. Thanks for pointing it out

Here's the double Matrix. Just to make it clearer.



We choose 100 as the smart number since everything is in percentage (Its marked in Orange in the screen shot). The Green colour is what is "Given"in the question. Rest everything is simple addition. Finally we get the required answered (Marked in Yellow).

Thank you, susheelh. Job well done at explaining! I intend to follow this approach for overlapping sets ... although, I am yet to encounter a problem where there are more than 2 sets that overlap.

+1 to your solution!

I am Glad that it helped!

There are loads of question with more then two sets overlap, I am sure you will find them.

As a general thumb rule (courtesy : MGMAT strategy guides) : for two set overlap use double matrix. For 3 set overlap, use Venn diagrams.



Sent from my iPhone using Tapatalk

I was thinking about the same as well. Like I said, I have not yet started working on Overlapping Sets questions just yet to evaluate the two approaches Thanks, bud!

Thanks, Such a help!!

We can use the equation:

Total = Stockholders + Employees - Both + Neither

100 = 62 + 47 - Both + 0

100 = 109 - Both

Both = 9

Thus, the percent of people at the meeting who were stockholders but not employees (i.e., stockholders only) is 62 - 9 = 53 percent.

Answer: B

I am a bit confused. I saw this question in the quant review after number 60 i think, so i was under the impression that it would be atleast above 600 level but i dont see thats the case.
reason to ask is that i am not too comfortable solving such questions, can someone comment on the difficulty level of this question ?

Total = Stockholders + Employees - Both;
100 = 62 + 47 - Both --> Both = 9;

Percent of stockholders, who were not employees is: Stockholders - Both = 62 - 9 =53.

Posted from my mobile device

Let's use the Double Matrix Method.
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).

Here, we have a population of attendees, and the two characteristics are:
- stockholder or not a stockholder
- employee or not an employee

Since we're not told the total number of attendees, and since we're trying to find a PERCENTAGE, let's assign a nice value to the total number of attendees
Let's say there are 100 attendees

Finally, since we're looking for the percentage of attendees who were stockholders but NOT employees, let's place a red star in that box to remind us of what we're trying to determine.



62 percent of those who attended the meeting were stockholders
This also means that the other 38 percent are NOT stockholders



47 percent were employees
This also means that the other 53 percent are NOT employees


At this point, we appear to have no more information to add to our diagram.
However, we also know that each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both
This means that there were ZERO people who were neither a stockholder nor an employee.
So, we can add this to our diagram.


Since the two boxes in the right-hand column must add to 53, we know that the top right box must have 53 people in it...



What percent were stockholders who were not employees?
Out of 100 attendees, 53 people were stockholders but not employees
In other words, 53% of the people were stockholders but not employees

Answer: D
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.

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: