Of the 200 math majors at a certain university, 30 percent w

Question

Of the 200 math majors at a certain university, 30 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 70 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer?

(A) 15
(B) 20
(C) 30
(D) 45
(E) 60

(A) 15
(B) 20
(C) 30
(D) 45
(E) 60

nave · Answer

30% of students are assigned to Monday and Wednesday = 0.3*200 = 60
70% of students are assigned to Tuesday and Thursday = 0.7*200 = 140

60% of students prefer Monday and Wednesday = 0.6*200 = 120
40% of students prefer Tuesday and Thursday = 0.4*200 = 80

Since we need the  least  number of students who will not be assigned to their preferred days, we shall fit in the  maximum  possible students as per their preference:
All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days. 
The remaining 60 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice. 
Answer is E.

LalaB · Answer

since we need to minimize the number of unhappy persons, we need to maximize the number of happy persons 
Thus, let 40% who prefer Tuesday and Thursday be happy among 70% (70-40=30 unhappy places are empty)
let fill in these 30 unhappy places with 60 % who prefer Monday and Wednesday
the rest of 60% (60-30=30%) i.e. 30% will be happy among 30 percent who prefer Monday and Wednesday

So, 30% unhappy ppl out of 200 = 60 unhappy ppl

Bunuel · Answer

"Stolen" question from OG: Discussed here: of-the-50-researchers-in-a-workgroup-40-percent-will-be-137538.html Another similar question to practice: of-the-200-employees-in-a-certain-company-25-percent-will-128189.html Hope it helps.

law258 · Answer

200 total

60 ADV Calc M/W --> 120 prefer this class 
140 ADV Calc T/Th --> 80 prefer this class

Assuming 60 of the 120 and 80 of the 140 get into the class they prefer, that leaves 60 students who do not get the class they prefer.

ScottTargetTestPrep · Answer

We see that 200 x 0.3 = 60 are assigned to Monday and Wednesday when 200 x 0.6 = 120 students prefer those days.

We also see that 200 x 0.7 = 140 are assigned to Tuesday and Thursday when 200 x 0.4 = 80 students prefer those days.

To minimize the number of students who are not assigned to the days they prefer, let’s assume that all the 80 students who prefer Tuesday and Thursday are indeed assigned to class on Tuesday and Thursday. Then, of the 120 students who prefer Monday and Wednesday, at least 120 - 60 = 60 students will have a class on days that they did not prefer.

Answer: E

sayan640 · Answer

Please find my solution diagram attached herewith.
PMW = Preferred Monday and WEdnesday;
PTTH = Preferred Tuesday and Thrusday ;
AMW = Assigned Monday and Wednesday 
ATTH = Assigned Tuesday and thursday.
We gotta minimise the highlighed portion i.e portion wherein people preferred Monday and WEdnesday but got 
assigned Tuesday and thursday. Also , include the portion wherein people preferred Tuesday and Thrusday but got 
assigned Monday and Wednesday.
HEnce the answer is E) 60.

Of the 200 math majors at a certain university, 30 percent w

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