[Akriti]

In a factory, where working in at least one department is mandatory, 78% are in operations,69% are in finance and87% are in HR. What is the maximum % of people who are working in all three?

Also the minimum for the same?

[Guest]

I guess you could make 3 intersecting sets for the 3 departments, then use to sets to get some equations like O + OF + OH + OFH = 78%, and using these equations and the fact that some sums cannot exceed 100%, you can find the maximum and minimum you're looking for. I won't tell the answer I got because I'm not sure it's right anyway. And if this this is your homework, you should have posted it in the homework section of the forum. I apologize in advance if my method is not correct.

[Guest]

the maximum for all three would be the same as the lowest percentage for any department, 69%.

The minimum would be infentessimal, or dependant on how many people there are in the company.

100 people, then 1%

1,000,000 people, less than one percent.

Wouldn't it be

[bonanova]

In a factory, where working in at least one department is mandatory, 78% are in operations,69% are in finance and87% are in HR.

What is the maximum % of people who are working in all three?

Also the minimum for the same?

13% are not in HR

31% are not in finance

22% are not in operations.

These could be all different people, making 66% not in all three. Minimum therefore is 34%

On the other hand, three groups can maximally overlap. Maximum therefore is 69% - the size of the smallest group.

[Guest]

maximum no. is 69% and minimum is 1

[Guest]

Max - 69% and Min - 34%.

[Akriti]

Sorry! no correct answers yet.

[k-man]

I'm with Bona and amateur on the minimum answer - 34%.

The maximum, however can only be 67%. This comes from the fact that if the maximum was 69% then that leaves only 9% for operations people and 18% for HR people. This accounts for only 96% of people. Assuming these are the only 3 departments at the factory 67% can work in all three, 2% work only in finance, 11% work only in operations and 20% work only in HR.

[Guest]

I'm with Bona and amateur on the minimum answer - 34%.

The maximum, however can only be 67%. This comes from the fact that if the maximum was 69% then that leaves only 9% for operations people and 18% for HR people. This accounts for only 96% of people. Assuming these are the only 3 departments at the factory 67% can work in all three, 2% work only in finance, 11% work only in operations and 20% work only in HR.

Good One. Akriti - thanks for posting and k-man - thanks for correcting.

I correct myself on Max %. 67% is the correct answer.

[Guest]

Let O be the percentage of people who work only in operations, OH the percentage who works in operations and HR, OFH the percentage who works on all 3, and so on.

We have that:

O + OH + OF + OFH = 78%

F + FH + OF + OFH = 69%

H + FH + OH + OFH = 87%

We also know that:

O + H + F + OF + OH + FH + OFH = 100%

Adding the first 3 and subtracting the last, we're left with:

OH + OF + FH + 2OFH = 134%

From the fourth equation, we know that OH + OF + FH + OFH is smaller than, or equal to 100% (since O, F and H are not negative). So we can make:

100% + OFH = 134%

OFH = 34%(minimum)

Now, if we make OH = OF = FH = 0:

0 + 2OFH = 134%

OFH = 67%(maximum)

So there you have it like the other guys said, unless I missed something.

[Akriti]

thanx guys!!

[Guest]

Max: 67% works in all depts, Min: 0% works in all depts

Since you are seeking only the %, then chance of all three working will be from 0% to 67%.

0 <= OFH <= 67

Edited November 18, 2010 by aaronbcj