The Number of students learning Three subjects are as follows
Maths = 40
English = 50
Science = 35
If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?  Select
A) 0
B) 1
C) 25
D) 35
E) 45
Let's assume the following :   a = Only Math   b = both Math and English   c = Only english   d = English and Science   e = Only Science   f = Math and Science   g = All three ( = 0 )   Now, to make the Only subjects (a+c+e) minimum, we need to maximize the both subject (b+d+f)   Since, we have minimum no. of students in science, we can consider Only Science(e) = 0 and Both(English and Science &amp; Math and Science) = d+f = 35   also, we have a+b+f = 40 --(1)   and , b+c+d = 50 --(2)   Adding (1) and (2),   a+2b+c+f+d = 90;   or a+2b+c = 55   Now, we have to maximize b and minimize a and c,   if a+c = 0 ==&gt; 2b =55 -- Not possible.   If a+c =1 ==&gt; 2b = 54 =&gt; b=27, Possible.   So, we can say a+c+e = 1(Minimum value),   Hence 1.
<result>B</result>
The Number of students learning Three subjects are as follows
Maths = 40
English = 50
Science = 35
If the Number of students learning exactly two subjects is maximum and no student learns all the three subjects, then what is the minimum number of students learning exactly one subject?