Answer to Office Social Question

Question:
Of the 80 colleagues in an office, 25 are going to an event, 15 are working late and 13 are volunteering. 3 are going to an event and working late; 4 are working late and volunteering; 2 are going to an event and volunteering; and none are doing all three. How many colleagues are not going to an event, working late, or volunteering?

Answer using Mental Math
Part One: Understand the Language

The hardest part is to understand this sentence in the question: "25 are going to an event, 15 are working late and 13 are volunteering."


"25 are going to an event" DOES NOT MEAN "25 colleagues are only going to an event and not take part in other activity".

"25 are going to an event" MEANS "25 colleagues are going to an event and some of them may also take part in the other one or two remaining activities.  In other words:
Employees GOING TO AN EVENT ONLY + Employees GOING TO AN EVENT and working late + Employees GOING TO AN EVENT and volunteering + Employees doing all three: GOING TO AN EVENT, working late and volunteering = 25

Therefore,
Number of Employees GOING TO AN EVENT ONLY = 25 - (Employees GOING TO AN EVENT and working late + Employees GOING TO AN EVENT and volunteering +  Employees doing all three) = 25 - (3 + 2 + 0) = 20
The same interpretation should apply to the rest of the sentence. 

Number of Employees WORKING LATE ONLY = 15 - (Employees WORKING LATE and going to an event + Employees WORKING LATE and volunteering +  Employees doing all three) = 15 - (3 + 4 + 0) = 8

Number of Employees VOLUNTEERING ONLY = 13 - (Employees VOLUNTEERING and working late + Employees VOLUNTEERING and going to an event +  Employees doing all three) = 13 - (4 + 2 + 0) = 7
Once you understand the language used in the question correctly, finding the answer is easy.
Part Two: The Solution

The total number of colleagues in the office is 80.

80 = number of employees who ARE NOT taking part in ANY ACTIVITY (Group Zero) + number of employees who ARE TAKING PART IN ONE ACTIVITY ONLY (Group One) + number of employees who are taking part in TWO ACTIVITIES (Group Two) + number of employees who are taking part in ALL THREE ACTIVITIES (Group Three)
Calculating Group One (number of employees who ARE TAKING PART IN ONE ACTIVITY):
Group One = Number of Employees Going to An Event ONLY + Number of Employees Working Late ONLY + Number of Employees Volunteering ONLYGroup One = 20 + 8 + 7 = 35
Calculating Group Two: (Number of Employees Who Are Taking Part in Two Activities)
Group Two = Number of Employees Going to An Event and Working Late + Number of Employees Working Late and Volunteering + Number of Employees Going to an Event and VolunteeringGroup Two = 3 + 4 + 2 = 9
Calculating Group Three: (Number of Employees Who Are Taking Part in All Three)
As stated in the question, number of employees who are doing all three equals ZERO (0)Group Three = 0

Group Zero = 80 - (Group One + Group Two + Group Three)
Group Zero = 80 - (35 + 9 + 0) = 36

Answer: Number of colleagues not taking part in any activity (going to an event, working late or volunteering) is 36.