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NDA 2020 Maths · Mathematics · Sequences and Series · hard

The arithmetic mean of two positive numbers is 13 and their geometric mean is 12. Their harmonic mean is

Single correct option

The arithmetic mean of two positive numbers is 13 and their geometric mean is 12. Their harmonic mean is
  1. A. 16912\dfrac{169}{12}
  2. B. 12
  3. C. 252\dfrac{25}{2}
  4. D. 14413\dfrac{144}{13}
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Answer: (D) 14413\dfrac{144}{13}

For two positive numbers GM2=AM×HM\text{GM}^2=\text{AM}\times\text{HM}, so HM=14413\text{HM}=\dfrac{144}{13}. Check: the numbers are 8 and 18, and 2⋅8⋅1826=14413\dfrac{2\cdot8\cdot18}{26}=\dfrac{144}{13}. The value 169/12169/12 is AM2/GM\text{AM}^2/\text{GM}.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake