Bunuel wrote:

Given that \(m^2 - 2m -15 = 0\) and \(n^2 - 3n - 10 = 0\), where m ≠ n, what is the product of m and n?

(A) -15

(B) -10

(C) -6

(D) 6

(E) 15

Factorizing the two equations

\(m^2 - 2m -15 = 0\) -> \(m^2 - 5m + 3n -15 = 0\) -> \((m-5)(m+3) = 0\) -> \(m = 5 or -3\)

\(n^2 - 3n - 10 = 0\) -> \(n^2 - 5n + 2n - 10 = 0\) -> \((n-5)(n+2) = 0\) -> \(n = 5 or -2\)

Therefore, the product of m and n such that m≠n is (-3)(-2) =

6(Option D)
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