Students from four sections of a class accompanied by respective class teachers planned to go for a field trip. There were nineteen people in all. However, on the scheduled day one of the four teachers and a few students could not join the rest. Given below are some statements about the group of people who ultimately left for the trip.
I: Section A had the largest contingent.
Il: Section B had fewer students than Section A.
Ill: Section C's contingent was smaller than Section B.
IV: Section D had the smallest contingent.
V: The product of the number of student from each section is a multiple of 10.
VI: The number of students from Section C is more than 2.
VIl. The product of the number of students from each section is a multiple of 24.
VIll. The largest contingent has more than 4 students.
IX: Each section contributed different number of students
The statements that taken together can give us the exact number of students from each section:

Option A: we get that A>B>C>D and C>2

Option B: we get A is the largest, C>2, A>4 and every section has a different number of students.

Option C: we get that A>B>C>D, C>2 and A*B*C*D = 10n

Option D: we get A>B>C>D, C>2 and A*B*C*D = 24n

Option E: we get A is the largest, D is the smallest, C>2, A*B*C*D = 24n, and each section has a different number of students.

Statement 9 tells us that each section contributes a different number of students and thus this statement is a must in figuring out each section’s strength.

Thus, options A, C and D are eliminated. From option B we cannot figure out any value since we don’t have any relation between their values. Hence, option B is eliminated.

Option E tells us about the largest and smallest section, also provides a relation between all their values which can be used to find out possible solutions and also tells us that each section contributes a different number of students which can be used to eliminate the undesirable results.

Thus, option E is the answer.