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Question

The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic mean?

This question was previously asked in
CDS I 2020 Elementary Mathematics Previous Year Paper (02-Feb-2020)
The correct answer is

14.4

For two numbers, the arithmetic, geometric and harmonic means obey this identity.

\(G^2=AH\Rightarrow A=\frac{G^2}{H}=\frac{12^2}{10}=14.4\)

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Important Questions from Relations between AM, GM, HM

  1. If \(a_1, a_2, a_3,...,a_n\) are positive real numbers whose product is a fixed number C, then the minimum value of \(a_1+a_2+...+a_n\) is

  2. Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?

  3. Consider the following statements:

    1. cos θ + sec θ can never be equal to 1.5.

    2. tan θ + cot θ can never be less than 2.

    Which of the above statements is/are correct?
  4. Consider the following measures of central tendency for a set of N numbers:

    1. Arithmetic mean.

    2. Geometric mean.

    Which of the above uses/use all the data?

  5. The harmonic mean of two number is 4, Their arithmetic mean A and the geometric mean G satisfy the relation 2A + G 2= 27, then the two numbers are

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