SOLUTION: Electronic Devices In a survey of college students, it was found that….. 356 owned an iPod 293 owned a laptop 285 owned a gaming system 193 owned an iPod and a laptop 200 owne

So you'll learn how to do this kind of problem, I am changing all the numbers
so you'll have to go through it yourself and figure it all out.  You won't
learn anything if I do the exact same problem for you.  Below are the numbers
I am using.  The words are the same but the numbers are different.  I'll go
through it step by step:  

Electronic Devices In a survey of college students, it was found that…..
(1)  343 owned an iPod
(2)  269 owned a laptop
(3)  268 owned a gaming system
(4)  179 owned an iPod and a laptop
(5)  188 owned an iPod and a gaming system
(6)  122 owned a laptop and a gaming system
(7)  59 owned an iPod, a laptop and a gaming system
(8)  29 owned none of these devices

Nearly always in these problems, the clues are given 
in the reverse order from the order in which you use them
to fill in the Venn diagram.  So let's start with (8).

(8)  29 owned none of these devices
That refers to the region with z, outside the circles.
So we write z=29 in the outer region at the bottom left.



Next we look at clue (7)
(7)  59 owned an iPod, a laptop and a gaming system 
That's the region in the middle with w, for it is common
to all three circles. So we write w=59



Next we look at clue (6)
(6)  122 owned a laptop and a gaming system
That is the two regions with w and x because they are the
two regions in common to circles L and G. We already have w=59,
so to find x, we subtract 122-59=63, and so x=63.  We write
that in:



Next we look at clue (5)

(5)  188 owned an iPod and a gaming system
That is the two regions with w and v because they are the
two regions in common to circles I and G. We already have w=59,
so to find v, we subtract 188-59=129, and so v=129.  We write
that in:



Next we look at clue (4)

(4)  179 owned an iPod and a laptop
That is the two regions with w and t because they are the
two regions in common to circles I and L. We already have w=59,
so to find t, we subtract 179-59=120, and so t=120.  We write
that in:



Next we look at clue (3)

(3)  268 owned a gaming system
This is the entire G circle consisting of v,w,x and y
We already hanve v=129, w=59, and x=63. So we add those
and subtract from 268 to find y. v+w+x=129+59+63=251, and
we subtract that 268-251=17, so y=17.  We write that in:



Next we look at clue (2)

(2)  269 owned a laptop
This is the entire L circle consisting of t,u,w and x
We already hanve t=120, w=59, and x=63. So we add those
and subtract from 269 to find u. t+w+x=120+59+63=242, and
we subtract that 269-242=27, so u=27.  We write that in:



Next we look at clue (1)
(1)  343 owned an iPod
This is the entire I circle consisting of s,t,v, and w
We already hanve t=120, v=129, and w=59. So we add those
and subtract from 343 to find s. t+u+x=120+129+59=308, and
we subtract that 343-308=35, so s=35.  We write that in:



Now that we have all 8 regions filled in we can answer
any question:

A)	How many college students were surveyed?

We just add all the ones in all 8 regions: 
s+t+u+v+w+x+y+z = 35+120+27+129+59+63+17+29 = 479 

        Of the college students surveyed, how many owned
B)	An IPod and a gaming system, but not a laptop?

That's all the ones in circles I and G that are not in
circle L. Those are s, u and y (they are not in L)
s+u+y = 35+129+17 = 181.


C)	A laptop, but neither an IPod nor a gaming system?

That's just the ones in circle L that are NOT in circle I and
not in circle G.  That's just u only! u=27.

Now, go back through it and put your numbers in.

Edwin