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2024 AMC 10B Problem 12

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2024 AMC 10B Problem 12AMC 10 Step by Step

Name: Date: September 13, 2026

Basic Counting · difficulty 3 of 5 · about 4 min · position P11-15

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)
$100$

2024 AMC 10B Problem 12

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