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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression

The arithmetic mean of two positive numbers is 10 and their geometric mean is 8. What is their harmonic mean?

The harmonic mean is 6.4. For two positive numbers, the square of the geometric mean equals the product of the arithmetic and harmonic means. So 8 squared, 64, divided by the arithmetic mean 10 gives 6.4, which is below the GM as it must be.

  1. A6.4Correct
  2. B9
  3. C12.5
  4. D7.2

Explanation

For two numbers, GM squared = AM x HM. So 64 = 10 x HM, giving HM = 6.4. Choosing 12.5 comes from dividing AM by GM squared the wrong way (100/8 style error), i.e. computing AM²/... incorrectly; HM must be less than GM, so 12.5 is impossible.

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