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20 Jun 2019, 02:30
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Difficulty:
95%
(hard)
Question Stats:
28% (03:18) correct
72%
(02:45)
wrong
based on 178
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In a survey on the popularity of magazines A,B and C among 100 pupils, 39 pupils like A, 36 like B, 45 like C, 14 like A and B only, 11 like B and C only, 5 like A and C only. Find the maximum number of pupils who do not like any of the magazines.
A) 10
B) 12
C) 20
D) 32
E) 48
A) 10
B) 12
C) 20
D) 32
E) 48
20 Jun 2019, 11:44
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It's a very good problem.
Let 'x' pupil don't read any magazine and 'y' pupil read all 3 magazines
100-x= 39+36+45-14-11-5-2y
x=10+2y
We need to maximize the value of 'y' in order to maximize the value of x
y can be maximize when 11-y=0 or y=11
{If y were greater than 11, the pupil who read only magazine would be negative} You can clearly see that in the diagram below
The maximum number of pupils who do not like any of the magazines= 10+2*11=32
Let 'x' pupil don't read any magazine and 'y' pupil read all 3 magazines
100-x= 39+36+45-14-11-5-2y
x=10+2y
We need to maximize the value of 'y' in order to maximize the value of x
y can be maximize when 11-y=0 or y=11
{If y were greater than 11, the pupil who read only magazine would be negative} You can clearly see that in the diagram below
The maximum number of pupils who do not like any of the magazines= 10+2*11=32
Attachments
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General Discussion
20 Jun 2019, 05:47
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Arvind42
\(None_{max} =\) 100 - (39+36+45-14-11-5-2*0(all three)) = 10
Answer: Option A
