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

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 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%

Kudos for a correct solution.

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

GMATinsight · Accepted Answer

Answer: Option D

Check the steps below

ske · Answer

Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M were stockholders and 47% of M or 0.47M were employees, it follows that 0.62M + 0.47M = 1.09M were either stockholders, employees, or both. Since 1.09M exceeds M, the excess 1.09M − M = 0.09M must be the number of attendees who were both stockholders and employees, leaving the rest 0.62M − 0.09M = 0.53M, or 53%, of the meeting attendees to be stockholders but not employees. The correct answer is D. :-D

reto · Answer

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

Stockholder only = 62 - 9 = 53

Answer D.

herbgatherer · Answer

Hope this representation helps

devctg · Answer

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

mindi · Answer

it can be done like this

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

Stockholder only = 62 - 9 = 53

Answer D.

TimeTraveller · Answer

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

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

EMPOWERgmatRichC · Answer

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:  D

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

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 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 EXTRA PRACTICE QUESTION https://www.youtube.com/watch?v=DsbPUSH_Wu4 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

satheshshiva · Answer

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

sagargoyal · Answer

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.

kartikesh8375 · Answer

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%

Kudos for a correct solution.

(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

ScottTargetTestPrep · Answer

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

ArnauG · Answer

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%.

bumpbot · Answer

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