Mental Math: Office Social Question (posted by Accounting Principles)

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 = 35Calculating 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 = 9Calculating 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 = 0Group 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.

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.

Saturday Circuit Fuse

My apartment home has recently experienced power outage in one power outlet. So I phoned in to the maintenance office. When the janitor arrived, he PULLED OUT HIS TOOL and OPENED MY POWER SOURCE CLOSET. He said, "Wow, you have 6 circuits in this housing; that is a lot of power for the house, dude! But one of the circuit fuse got burnt."

I responded, "There are 6 ...of them here. They all look same-same to me. I am not familiar with electrical engineering. Can you please just point out the one that is burnt?" He replied, "The Red one".

I said, "Now, it's easy. There's only one RED. I could identify it. Can I touch it?"

He responded, "Normally, you would't be able to touch it as you might get shocked. But I have turned off the power. So yeah, you can go ahead and touch it."

I asked, "Am I supposed to pull or push it here?"

He instructed, "You just rotate it 360 degrees".

So I managed to take it out. My apartment home is cold, but this fuse feels so warm in my palm. I asked him "Can I smell it?"

He smiled astonishingly, "I don't see why not!?"

So I placed it near my nose, and it smells like burned iron or magnet of some sort. A little bit weird...

I WEIGHed UP ON THIS WITH HIM, "Is this smell bad for my health?".

He laughed, "Of course, it wouldn't be bad for you, unless you spend 24 hours staying in this closet and smelling this stuff. I do it all the time, and LOOK, I feel quite like a dandy - pretty GOOD SHAPE here isn't it?

I FELT SATIFIED WITH HIS ANSWER, so I placed the fuse back to its housing." I asked, "So when are we able to FIX THIS?

He said, "This thing needs to be special ordered. It is not a common piece of hardware. The part will COME IN ON SATURDAY."

I advised him, "My TV is hooked to the power outlet without power. I need to watch a special show AROUND 11:00 PM on Saturday. Hope IT WILL BE FIXED AT THAT TIME."

He assured, "Sure thing! You can TRUST* my track record of getting things done. May I ask for the name of that show."

I revealed, "Five Sheeps and a Red Witch".

Powerball #Broken_Dream #Empty_Promise #Blood_Greed #Stuck_Like_Glue #Incredible_Machine #Organized_Crime_Ring