Each person who attended a company meeting was either a stockholder in

Overlapping Sets question: Total (100) = 62 + 47 - 9 (Both)

Stockholder only = 62 - 9 = 53

Answer D.

Hope this representation helps

suppose stockholder in the company = s
employee in the company = e
both = b
as per question
=> s + b = 62
=> e + b = 47
then
stockholder in the company + employee in the company - both = 100%
(s+b) + (e+b) -b = 100
=> b =9
now stockholders who were not employees => (s + b) - b
=> 62 -9 => 53

it can be done like this

Overlapping Sets question: Total (100) = 62 + 47 - 9 (Both)

Stockholder only = 62 - 9 = 53

Answer D.

Stockholders = 62, Employees = 47, both = 62+47-100 = 9.

Stockholders but not employees = 62-9/100 = 53%. Ans - D.

Hi All,

This is essentially an Overlapping Sets question that does not have a "neither" group. As such, it can be solved in a couple of different ways. Here's how you can use standard Overlapping Sets formula to get to the correct answer:

Total = (Group 1) + (Group 2) - (Both) + (Neither)

Group 1 = % that are stockholders
Group 2 = % that are employees

100% = 62% + 47% - (Both) + 0%
100% = 109% - (Both)
Both = 9%

So 9% of the total attendees are BOTH stockholders AND employees. We're asked for the percent who were stockholders but NOT employees:

62% - 9% = 53%

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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

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:


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

We know the formula,

Group 1 + Group 2 - Both +Neither = Total

Let us assume Total as 100 since all are percentages.

62 + 47 - Both + 0 = 100
Both =9

We are asked the number of Stock holder company alone (Group A)

Group A Alone = Group A - Both

= 62-9
=53

I feel the answer can be arrived really quick. Given the earlier condition, % employee are 47% so % not employees (means stockholders) = 53% (100-47) which is the answer. Correct me if I'm wrong with my approach.

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 those who attended the meeting were stockholders and 47 percent were employees, what percent were stockholders who were not employees?

(A) 34%
(B) 38%
(C) 45%
(D) 53%
(E) 62%

100% = 62 % + 47% - both + nor
'we have to find both
and nor is zero as no information is given

so
62+47 = 109
-9 = -both
leads to 9 = both
so 62%- 9% = 53%
hence D

Solution:

We can use the formula:

Total = Stockholders + Employees - Both + Neither

100 = 62 + 47 - Both + 0

100 = 109 - Both

Both = 9

We see that 9% of the attendees are both stockholders and employees. Since 62% of the attendees are stockholders, then 62 - 9 = 53% of the attendees are stockholders but not employees.

Answer: D

To determine the percentage of attendees who were stockholders but not employees, we need to find the difference between the percentage of stockholders and the percentage of attendees who were both stockholders and employees.

Given:
Percentage of attendees who were stockholders = 62%
Percentage of attendees who were employees = 47%

Let's denote:
S = Percentage of stockholders who attended the meeting
E = Percentage of employees who attended the meeting
SE = Percentage of attendees who were both stockholders and employees (overlap)

We can represent the situation using the formula:

Total attendees (T) = S + E - SE

Substituting the given values:
T = 62% + 47% - SE = 109% - SE

Since T represents the total percentage of attendees, it is equal to 100%.

100% = 109% - SE

Simplifying the equation, we find:
SE = 109% - 100% = 9%

Therefore, 9% of the attendees were both stockholders and employees.

To find the percentage of attendees who were stockholders but not employees, we subtract the percentage of attendees who were both stockholders and employees from the percentage of stockholders:
Percentage of stockholders who were not employees = S - SE = 62% - 9% = 53%

Therefore, the answer is (D) 53%.

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