set theory

Hi Imsukhi,

Is there any info regarding the total number of students who participated in the survey? That's the missing link in my solution.

Hi vivek,

The Question above is complete and it appears in the same text in two diff books.

4) How many students use all the three type of pen and none??
a)15,15 b)10,20 c)20,10 d)5,25 e) 30,0

Soln.

total no of ball pen users =
only ball pen users +
(ball pen + ink pen) users +
(ball pen + gel pen) users +
(ball pen + gel pen + ink pen) users

let users who do not use any of the 3 pens be x

from the data
total no of ball pen users = 85
only ball pen users = 75 - x
(ball pen + ink pen) users = 10
(ball pen + gel pen) users = 20
(ball pen + gel pen + ink pen) users = 30 - x

85 = 75 -x + 10 + 20 + 30 - x
2x = 50
x = 25 = users who do not use any of the 3 pens

hence
(ball pen + gel pen + ink pen) users = 30 - x = 5

hence option D

Data is insufficient for all other questions.
I think total no. of students surveyed was to be motioned for solving all the others.
let (gel pen + ink pen) users be y
y could range from 0 to 90, according to the restrictions placed by given data

1) How many students use at least one of the three type of pens
= 275 - y
2) How many students use ball pens or both ink pen and gel pen only ?
= 85 + y
3) How many students use both ball pen and ink pen?
= 5 + y
5) What is the difference in the number of students who use at least two and the one who use at least one o f the three?
= 240 - 2y

Could not use elimination also for these since multiple options satisfy for a non negative y.