Problem Solving

A certain college has a total of 400 seniors, each majoring in exactly one of six subjects. A minimum of 20 seniors major in each of the six subjects. If three-quarters of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?

A.80
B.50
C.60
D.75
E.100

Please help to explain.

IMO 100
. 1 2 3 4 5 6
20 20 20 20 20 20 .....minimum for each subject
.....300...........


3/4of 400 = 300 major in one of four subjects (1,2,3 &4)
remaining two subject 5&6 = 400-300=100 = greatest no. majoring in one of the other two subjects (5&6)

pls confirm the OA

IMO E.

b/c three quarters of the seniors major in 1 of the 4 subjects. That means 3/4*400=300 students major in one of the 4 subjects. So the most number of students that can graduate in the remaining two subjects is 100.

Hope I dint misunderstand the actual question.

I would go with 80 because there are remaining 2 subjects and it says A minimum of 20 seniors major in each of the six subjects.

100-20 = 80 left

Regards,
CR

cramya wrote:Hope I dint misunderstand the actual question.

I would go with 80 because there are remaining 2 subjects and it says A minimum of 20 seniors major in each of the six subjects.

100-20 = 80 left

Regards,
CR

Correct interpretation!

cramya wrote:Hope I dint misunderstand the actual question.

I would go with 80 because there are remaining 2 subjects and it says A minimum of 20 seniors major in each of the six subjects.

100-20 = 80 left

Regards,
CR

Seems like i misunderstood it & haven't yet understood it correctly:-(
I had thought the answer as 80 initially but the first line says "each majoring in exactly one of six subjects" ? The question is still not clear to me!

cramya wrote:Hope I dint misunderstand the actual question.

I would go with 80 because there are remaining 2 subjects and it says A minimum of 20 seniors major in each of the six subjects.

100-20 = 80 left

Regards,
CR

I got the same thing

SUBJECT 1-4 (Total of 300 students)
Subject 5
Subject 6
(Subject 5 and 6 combined have to equal 100, but each have to have at least 20 students). Thus, the most lopsided you can make 5 and 6 is 80-20. Thus 80 is the answer.

I blew this one.

If three-quarters of the seniors major in one of four subjects => 300 guys majored in one subject. Didn't quite understand that it's 300 distributed over 4 subjects.

- pradeep