Among 600 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
Pick one
A) 30  B) 90  C) 120  D) 172  E) 180
I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 180   Using your analysis:   We see that the total number of students who study either Maths or Sociology = 264 + 336 - 180= 
<gadget id="calculator">264 + 336 - 180</gadget>
<output>420</output>
420   So, in the image we know that the number of students in the zone with the black boundary= 420   Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)   And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w   Since the total number of students = 600, we can write:   420 +b+w= 600   Or,b+w= 600 - 420= 
<gadget id="calculator">600 - 420</gadget>
<output>180</output>
180   That is,b= 180 -w   So, the maximum value ofbwill happen forw= 0   This is how we get, the maximum value ofb= 180   180
<result>E</result>
Among 600 students, 56% study sociology, 44% study mathematics and 40% study biology. If 30% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?