What is the greatest possible number problem.

[billzhao]

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

Please help to explain. thanks.

[Uri]

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

Please help to explain. thanks.

IMO (B)
three-quarter of 400 = 300
so, 300 seniors major in 4 subjects
for the rest 2 subjects we have 100 seniors
if we allocate minimum number of students to one of these two subjects, then the other subject will have maximum possible number of students.
as per the question, at least 20 students will major each subject.
so the other subject can have max of 80 students majorinh in it.
what is the Official Answer (OA)?

[abhijeetsinghai]

what is OA ?

can anybody explain this ?

[Mr2Bits]

Is it just me or is the wording incorrect of this question?

If you have 400 students, 300 major in one subject and at least 20 major in each of the other 5 remaining subjects wouldn't that tap you out of students?

The logic seems off or maybe its just me.

If it's not, Answer D looks like a good guess to me.

[Mr2Bits]

https://www.beatthegmat.com/students-and ... 31301.html

[masuarezdl]

Is it just me or is the wording incorrect of this question?

If you have 400 students, 300 major in one subject and at least 20 major in each of the other 5 remaining subjects wouldn't that tap you out of students?

The logic seems off or maybe its just me.

If it's not, Answer D looks like a good guess to me.

No. Let me explain:

300 students for majors 1st to 4th.
20 for the 5th major.
20 for the 6th major.

Therefore, we have 340 students allocated, with 60 remaining. If no one else graduates from 4th or 5th, then the other major takes the full 60, adding up to the minimum 20 students that we said. That adds up to 80.

[Mr2Bits]

Is it just me or is the wording incorrect of this question?

If you have 400 students, 300 major in one subject and at least 20 major in each of the other 5 remaining subjects wouldn't that tap you out of students?

The logic seems off or maybe its just me.

If it's not, Answer D looks like a good guess to me.

No. Let me explain:

300 students for majors 1st to 4th.
20 for the 5th major.
20 for the 6th major.

Therefore, we have 340 students allocated, with 60 remaining. If no one else graduates from 4th or 5th, then the other major takes the full 60, adding up to the minimum 20 students that we said. That adds up to 80.

Got it now...cough medicine and studying dont work well.

I read it as 300 marjor in ONE instead of 300 major in subjects 1-4