nataras 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%
OA: A
I was able to back into this answer by doing the following (assuming 100 employees): 100-75 (winter)-20 (neither) = 5 (summer only). However is there a more technical way to solve this? Why does the Winter + Summer + Neither - Both formula not work for this question?[/img]
I would use a double-matrix here.
That said, we could also use the following formula:
Total = Winter + Summer - Both + Neither.
The big idea behind the formula above is to SUBTRACT THE OVERLAP.
When we count everyone who takes a winter vacation and everyone who takes a summer vacation, the overlap -- the percentage who take BOTH types of vacation -- is counted TWICE.
Thus, we must SUBTRACT the percentage who take BOTH types of vacation so that they are not double-counted.
Let the total = 100.
Plugging into the formula the given values for winter (75%), both (40%) and neither (20%), we get:
100 = 75 + Summer - 40 + 20
100 = 55 + Summer
Summer = 45.
Since a total of 45% take a summer vacation, while 40% take BOTH types of vacation, the percentage who take ONLY a summer vacation = 45-40 = 5.
The correct answer is
A.
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