Question 137
A group of 100 students from different countries meet at a mathematics competition. Each student speaks the same number of languages, and, for every pair of students $A$ and $B$, student $A$ speaks some language that student $B$ does not speak, and student $B$ speaks some language that student $A$ does not speak. What is the least possible total number of languages spoken by all the students?
(A) 9 (B) 10 (C) 12 (D) 51 (E) 100
(A) 9 (B) 10 (C) 12 (D) 51 (E) 100