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# Of the employees in Company X, 95% have desktop computer,

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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

Of the employees in Company X, 95% have desktop computer, [#permalink]  12 Dec 2007, 07:41
Of the employees in Company X, 95% have desktop computer, 75% have both Desktop and Laptop, and 60% have both Desktop and PDA. At least what percent of employees in the company have all of three kinds of devices?
a) 33%
b) 35%
c) 37%
d) 40%
e) 60%
Director
Joined: 12 Jul 2007
Posts: 864
Followers: 13

Kudos [?]: 224 [0], given: 0

Let 100 = number of employees at company X

95 have a desktop
75 have both a desktop and laptop
60 have both a desktop and PDA

Without drawing out circles I would solve it like this:

60 people have a desktop and PDA

There are 20 (95-75) people who have a desktop without having a laptop. So count that 20 people as part, but then 40 (60-20) will still have to have all 3.

The same thing works by starting with 75 people having a desktop and laptop. 75 have D and L and you can have 35 of them (95-60) not having a PDA. but that still leaves 40 (75-35) having all 3

in each case it's 75-(95-60) = 40 or 60 -(95-75) = 40

Senior Manager
Joined: 25 Jul 2007
Posts: 378
Location: Times Square
Schools: Baruch / Zicklin
Followers: 4

Kudos [?]: 37 [0], given: 148

I did the drawing circles method and got 40, choice D.
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

can someone draw out the Venn?
Director
Joined: 12 Jul 2007
Posts: 864
Followers: 13

Kudos [?]: 224 [0], given: 0

here is my hastily drawn MSPain Venn Diagram

I've filled in all the information we're given.

Assuming 100 employees...

75 have a desktop AND a laptop
60 have a desktop AND a PDA

but then they say 95 employees have a desktop.

We have 135 people already listed for D though. This means some of them have to be moved from a 2-item category to the all-3 category. By moving people into the center we get to count them for both lists (towards the 75 and the 60) while they still only take up 1 spot on the 95.

75+60 = 135 - 95 = 40

This means that 40 people must be counted in the middle for it to work.

We can take that 40 from the 75, the 60 or 20 from each. It doesn't matter, we've just found our answer that a minimum of 40% have all 3.
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 389 [0], given: 4

the center is unknown, the pink part should be expressed as 60%-x
Director
Joined: 12 Jul 2007
Posts: 864
Followers: 13

Kudos [?]: 224 [0], given: 0

75+60-x = 95
x = 40

I was just trying to simplify the diagram as much as possible. It's the same formula and the same answer.
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