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

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Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 14 Sep 2015, 07:36
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Question Stats:

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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%

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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 20 Oct 2015, 04:11
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Bunuel wrote:
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%

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Answer: Option D

Check the steps below
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 14 Sep 2015, 08:48
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ske wrote:
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%



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
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 20 Oct 2015, 08:50
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Bunuel wrote:
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%

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

Stockholder only = 62 - 9 = 53

Answer D.
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Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 09 Dec 2016, 13:34
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Hope this representation helps
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 10 Mar 2017, 21:05
1
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
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 14 Jul 2017, 09:01
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it can be done like this

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

Stockholder only = 62 - 9 = 53

Answer D.
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 14 Jul 2017, 09:45
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Stockholders = 62, Employees = 47, both = 62+47-100 = 9.

Stockholders but not employees = 62-9/100 = 53%. Ans - D.
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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 16 Jan 2018, 12:30
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%

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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 07 Sep 2018, 13:47
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Bunuel wrote:
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.


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.
Image


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


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

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.
Image

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...
Image


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:

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Re: Each person who attended a company meeting was either a stockholder in  [#permalink]

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New post 20 Sep 2018, 19:27
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
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Re: Each person who attended a company meeting was either a stockholder in &nbs [#permalink] 20 Sep 2018, 19:27
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