set theory

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 36
Joined: Thu Jun 20, 2013 7:58 pm
Thanked: 1 times

set theory

by Imsukhi » Tue Jun 25, 2013 9:41 pm
A survey has been conducted in a college on using the type of pen for writing. the results are as follows
Total number of ball pen users= 85
Total number of ink pen users= 105
Total number of gel pen users=125
No. Of students who use both ink pen and ball pen but no gel pen= 10
No. Of students who use both ball pen and gel pen but no ink pen=20
No. Of students who do not use ink pen or gel pen=75
No. Of students who do not use any or use all three=30

1) How many students use at least one of the three type of pens
a)215 B)245 C)275 D)270 e) 250

2) How many students use ball pens or both ink pen and gel pen only ?
a)90 b ) 110 c) 80 d) 85 e) 115

3) How many students use both ball pen and ink pen?
a)15 b) 25 c)20 d)30 e) none of these

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

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?
a)180 b)190 c)210 d)165 e) 150


Please explain in detail.
Source: — Problem Solving |

User avatar
Senior | Next Rank: 100 Posts
Posts: 67
Joined: Wed May 01, 2013 9:32 am
Thanked: 16 times
GMAT Score:690

by vivekchandrams » Wed Jun 26, 2013 4:06 am
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.

Senior | Next Rank: 100 Posts
Posts: 36
Joined: Thu Jun 20, 2013 7:58 pm
Thanked: 1 times

by Imsukhi » Wed Jun 26, 2013 5:07 am
Hi vivek,

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

Senior | Next Rank: 100 Posts
Posts: 32
Joined: Tue Jun 25, 2013 2:56 am
Thanked: 4 times

by luckypiscian » Wed Jun 26, 2013 7:21 am
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.

User avatar
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Mon Dec 23, 2019 1:23 am

by Rushan » Mon Dec 23, 2019 2:06 am
Imsukhi wrote:A survey has been conducted in a college on using the type of pen for writing. the results are as follows
Total number of ball pen users= 85
Total number of ink pen users= 105
Total number of gel pen users=125
No. Of students who use both ink pen and ball pen but no gel pen= 10
No. Of students who use both ball pen and gel pen but no ink pen=20
No. Of students who do not use ink pen or gel pen=75
No. Of students who do not use any or use all three=30

1) How many students use at least one of the three type of pens
a)215 B)245 C)275 D)270 e) 250

2) How many students use ball pens or both ink pen and gel pen only ?
a)90 b ) 110 c) 80 d) 85 e) 115

3) How many students use both ball pen and ink pen?
a)15 b) 25 c)20 d)30 e) none of these

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

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?
a)180 b)190 c)210 d)165 e) 150


Please explain in detail.