Each person who attended a company meeting was either a

Question

Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 47 percent were employees. What percent were stockholders, who were not employees?

A. 52
B. 53
C. 54
D. 55
E. 56

A. 52
B. 53
C. 54
D. 55
E. 56

Bunuel · Accepted Answer

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

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

Answer: B.

jaffa100 · Answer

https://i.imgur.com/MAA67rv.png

HarveyKlaus  Hope it helps. This is my first post!

GyanOne · Answer

100 = 62 + 47 - n(SnE)   
=> n(SnE) = 9

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

Option (B)

Charles_River · Answer

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!!!

Abhishek009 · Answer

USe venn diagram , matter of 5 secods

HarveyKlaus · Answer

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!

susheelh · Answer

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.

Blackbox · Answer

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?

susheelh · Answer

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. Screen Shot 2017-09-04 at 9.51.17 AM.png 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).

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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. 
 https://i.imgur.com/QottU16.png

62 percent of those who attended the meeting were stockholders  
This also means that the other 38 percent are NOT stockholders
 https://i.imgur.com/be907zm.png

47 percent were employees  
This also means that the other 53 percent are NOT employees
 https://i.imgur.com/6YL3nba.png

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.
 https://i.imgur.com/cmLSDkS.png

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...
 https://i.imgur.com/pl6W8oR.png

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:
 https://www.youtube.com/watch?v=jK-tiBrrf04

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=u5brADh1sIE

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=jllXP4NLCg8

ADisHere · Answer

Hi, A very dumb doubt 
but wanted to know why we did not take 53/62 *100. arent we asked what percent were stockholders, who were not employees 
I got the qs right with POE though

Bunuel · Answer

We are asked to find the percentage of non-employee stockholders  in the total group , which is calculated as Stockholders - Both. Using 53/62 * 100 would instead give the percentage of non-employee stockholders  among only the stockholders .

If the question intended to ask for the percentage of non-employee stockholders  among only the stockholders , it would likely be phrased as, “What percent  of the  stockholders were not employees?”

bumpbot · Answer

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