If 75 percent of the employees of a certain company take a winter

Here's a step-by-step approach using the Double Matrix method.

We have a population of employees, and the two characteristics are:
- take a winter vacation or don't take a winter vacation
- take a summer vacation or don't take a summer vacation

So, we'll set up our matrix as follows:

NOTE: Since we're need to find a PERCENT (rather than the actual number of people), we'll say that there are 100 employees altogether. This will make our calculations easier.

75 percent of the employees of a certain company take a winter vacation
If 75% TAKE a winter vacation, the remaining 25% DON'T take a winter vacation.
Since we've let 100 = the total number of employees, we can see that 75 take a winter vacation and 25 don't. We'll add this to our diagram:


40 percent take a winter and a summer vacation
So, 40 employees take a winter AND a summer vacation, which we can add to our diagram.



20 percent take neither a winter nor a summer vacation
Add that here:


what percent of the employees take a summer vacation but not a winter vacation
We'll place a heart in the box that represents the value we're trying to solve for.


IMPORTANT: Since the bottom 2 boxes must add to 25, we can see that the bottom left box must equal [spoiler]5[/spoiler].


Answer:A

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Answer should be 5% ie A

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Why cant we just stop at 45? X=45
Why this question is different from other overlapping question where we just stop at finding the X (X could be a or b or both or neither)
We subtract "both" only once

It is the difference between summer vacations (including winter) and only summer vacations (not in winters).

45 people take vacations in summer. 40 of them take vacation in winters too. Since we are looking for the number that take vacations in summer BUT NOT in winter, we get 45 - 40 = 5.

Using some of the high school set theory
n(a)=75
n(b)=40
n(aUb)=80
n(intersection)=75+40-80=35
n(onlyb)=40-35=5
Smash A

Winter Vacation: 75%
Winter + Summer= 40%
Neither= 20%
Summer=?

S+W-(W-S)+N=100
S+75-(40)+20=100
S+55=100
S=45

Summer -Winter +Summer=only summer
45-40=5

Answer A

A really good question. I got wrong (option E) because I was too hasty and forgot to minus off 40%.

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