Problem Solving

Hi rsarashi,

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

rsarashi 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'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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-maj ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-spee ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appl ... 70255.html
- https://www.beatthegmat.com/opening-nig ... 64869.html
- https://www.beatthegmat.com/at-least-10 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping ... 64092.html
- https://www.beatthegmat.com/mba/2011/05 ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-pe ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peo ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume- ... 69355.html
- https://www.beatthegmat.com/mba/2011/05 ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set- ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05 ... question-3

Cheers,
Brent

rsarashi 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%

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: D