2024 Mock AMC 12 - Problem 23

Let n be a positive integer. If for any distinct x_1, x_2, \dots, x_n \in \mathbb{R}, we can always find 1 \le i < j \le n such that

\frac{x_ix_j + 1}{x_j - x_i} \ge \sqrt{3}

what is the minimum value of n?

\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8

Erratum. As printed, this problem states i < j; the intended condition was i \neq j. This problem was voided and no answer choice is accepted.