If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer

by BTGmoderatorDC » Fri Mar 11, 2022 8:09 pm

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If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%

OA A

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Fri Mar 11, 2022 8:09 pm

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Re: If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer

by Brent@GMATPrepNow » Sat Mar 12, 2022 5:54 am

BTGmoderatorDC wrote: ↑
Fri Mar 11, 2022 8:09 pm
If 75 percent of the employees of a certain company take a winter vacation, 40 percent take a winter and a summer vacation, and 20 percent take neither a winter nor a summer vacation, what percent of the employees take a summer vacation but not a winter vacation?

A) 5%
B) 15%
C) 25%
D) 35%
E) 45%

OA A

Source: GMAT Prep

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.