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

BTGmoderatorLU wrote: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

The OA is E.

Please, can anyone assist me with this PS question? Thanks.

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

> 60% of students prefer Monday and Wednesday = 60% of 200 = 120
> 40% of students prefer Tuesday and Thursday = 40% of 200 = 80

We need the least number of students who will not be assigned to their preferred days, thus, we will assign the maximum possible students as per their preference.

Case 1: Assuming all of those who prefer Tuesday and Thursday are assigned Tuesday and Thursday

# of students who would NOT get their preferred days = 140 – 80 = 60

Case 2: Assuming all of those who prefer Monday and Wednesday are assigned Tuesday and Thursday

# of students who would NOT get their preferred days = 120 + (80 – 20) = 180

Since the question asks for the lowest possible number of math majors who will NOT be assigned to the days they prefer, the answer is 60!

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorLU wrote: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

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