In a survey of 200 employees of a company regarding their 401(k) investments, th

Question

In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained. 141 had investments in stock funds. 91 had investments in bond funds. 60 had investments in money market funds. 47 had investments in stock funds and bond funds. 36 had investments in stock funds and money market funds. 36 had investments in bond funds money market funds 5 had investments only in some other vehicle Q1. How many of the employees surveyed had investments in all three types of funds? Q2. How many of the employees had investments in stock funds only?

Explanation / Answer

The trick here is to see how a Venn diagram can assist you with the numbers.
It is not possible to draw one here, but set one up as follows:
3 interlocking circles for the 3 funds types, then work backwards up the list
of statements from the "22 had all 3 funds" - this is the number in the centre
where the 3 circles interlock. The next 3 statements up the list allow you to
work out the numbers for where 2 circles interlock (remember that 22 of those
numbers have already been placed in the centre zone, so the numbers are ==>
36-22=14 for where bond & money market interlock
36-22=14 for where stock & money market interlock
47-22=25 for where stock & bond interlock
You can then use the top 3 statements to work out the numbers that are in a
single circle (set)> for stock the number is 141-(22+14+25)=80
for bond the number is 91-(22+14+25)=30
for money market the number is 60-(22+14+14)=10
lastly, work out the number that goes in the rectangle (universal set) but
not in the circles ==> 200-(80+30+10+25+14+14+22)=5

a) 22

b) 80

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