IMAT 2022 question 7

There are 10 students in a class and they like visiting each other. A visit means that one student
visits the home of another student. We know that each student in the class has visited the
same number of students. No two students in the class have both visited each other.
What is the maximum number of students that a student in this class could have visited?
A) 4 B) 2 C) 5 D) 8 E) 9

Hi!

The answer is A).
I’m not sure how to visualize the question properly, this is my work, i’d love to compare to someone else’s strategy to solve.
Thanks!

1 Like

Why the answer can’t be D) 8 ?

ok i think this is the answer
it’s a permutations problem

nPr = n!/(r!(n-r)!) with n = 10 and r = 2
= 10!/2!8! = 9 * 5 = 45 total visits
45/10 = 4,5 visits per student
since the answer must be an integer, each students visits a max of 4 other students