venn diagram problem

[shahab03]

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%

Not sure how to tackle this question
D = 95
D n L = 75
D n P = 60

if X is the percent of employees with all three things
then

X = D n L n P
so 95 = D only -75 -60 -x ...


Answer is D. But not sure how to go from here.

[carrotbaba]

see its fairly easy if u understand it. (DuLuP)=(D)+(L)+(P)-(DnP)-(DnL)-(LnP)+(DnPnL) right using this formula we substitute. 95-75-60(others take as 0)+ (DnPnL)(thats what we want) -40+(DnPnL)=DuLuP it has to be alteast 0 -40+x>=0 therefore x has to be atleast 40%. hope that helps.

[shahab03]

why are you taking (L) and (P) as 0.

I am not following... would you please explain... thanks

[iisan]

Of the people who have the desktop computers, 20 do not have laptop computers. The maximum number of people who can have both desktop and PDA, but not laptop can be 20. Therefore, the number of people who will have all three = 60 - 20 = 40 Ans D.

[bmwhype]

can someone map out the venn?

[bmwhype]

ok figured it out

D is comprised of D only + DB + DL
DB consists of DB + DBL

[windriver]

Let x be the number who won all 3

95 = only desktops + 75-x + x + 60-x
=> x = 40 + only_desktops
To find the least value of x, only_desktops has to be 0.
=> x = 40

[yowas]

None of these explanations make sense at all.

Can someone please start over from the beginning, either using the DnPnL formula above or posting a picture of a venn diagram.

I still have not came up with a concrete way to do these.

Thanks.

[diya123]

ok i got a simple method for you.
draw 3 intersecting circles (Hope thy familiar with venn diagrams)
lets name them D P and L. now outside D write 95.
the portion bet D and L is 75 and that between D and P is 60.
NOw form the figure, you can make out a portion where all 3 circles intervene. this is x.
Now with respect to circle D we can write what the 95 consists of the following

95 =75+60 -x (subtract x as it has already been included in 75+60)
and x is the answer =40
hope his helps..

[anilmanu]

ok i got a simple method for you.
draw 3 intersecting circles (Hope thy familiar with venn diagrams)
lets name them D P and L. now outside D write 95.
the portion bet D and L is 75 and that between D and P is 60.
NOw form the figure, you can make out a portion where all 3 circles intervene. this is x.
Now with respect to circle D we can write what the 95 consists of the following

95 =75+60 -x (subtract x as it has already been included in 75+60)
and x is the answer =40
hope his helps..

Yep... Venn is the right way..