Answer: 8.12.

The relationship between arithmetic, harmonic, and geometric means is given by: arithmetic mean × harmonic mean = (geometric mean)² Given: - Arithmetic mean = 8.90 - Geometric mean = 8.50 We can solve for harmonic mean: 8.90 × harmonic mean = (8.50)² 8.90 × harmonic mean = 72.25 harmonic mean = 72.25 ÷ 8.90 harmonic mean = 8.11798 ≈ 8.12 Alternatively, we can use the inequality relationship: harmonic mean < geometric mean < arithmetic mean (for positive values that are not all equal). Since geometric mean = 8.50 and arithmetic mean = 8.90, the harmonic mean must be less than 8.50, which eliminates options B (8.63) and C (9.30). Only option A (8.12) satisfies this inequality.

Author: LeetQuiz Editorial Team