zxcvbnmas wrote:
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%
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 vacationIf 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 vacationSo, 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 vacationAdd that here:
what percent of the employees take a summer vacation but not a winter vacationWe'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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Brent Hanneson – Creator of gmatprepnow.com
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