If the arithmetic mean between two numbers is 64 and the Geometric Mean between them is 16. The Harmonic mean between them is

Option b: 4. Solution: Step 1: Apply the formula GM² = AM × HM. text{HM} = frac{text{GM}^2}{text{AM}} = 16^2/64 = 256/64 = 4 The Harmonic Mean = 4 = Option B. Note: The exam key says A (64), but mathematically HM = GM²/AM = 256/64 = 4 (Option B). Hence, Option B is the correct answer.

If the arithmetic mean between two numbers is $64$ and the Geometric Mean between them is $16$. The Harmonic mean between them is

The correct answer is Option b: $4$. **Step 1: Apply the formula GM² = AM × HM.** $$\text{HM} = \frac{\text{GM}^2}{\text{AM}} = \frac{16^2}{64} = \frac{256}{64} = 4$$ The Harmonic Mean = $4$ = **Option B**. Note: The exam key says A ($64$), but mathematically HM = GM²/AM = 256/64 = 4 (Option B). Hence, **Option B** is the correct answer.

Central Tendency & DispersionMTP June 24 Series IIIQuestion 3071 of 473

All Questions

If the arithmetic mean between two numbers is $\displaystyle 64$ and the Geometric Mean between them is $\displaystyle 16$ . The Harmonic mean between them is

Options

\displaystyle 64

\displaystyle 4

\displaystyle 16

\displaystyle 40

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Correct Answer

✅ Option b — $\displaystyle 4$

All Options:

A $\displaystyle 64$
B $\displaystyle 4$
C $\displaystyle 16$
D $\displaystyle 40$

Detailed Solution & Explanation

**Step 1: Apply the formula GM² = AM × HM.**

\text{HM} = \frac{\text{GM}^2}{\text{AM}} = \frac{16^2}{64} = \frac{256}{64} = 4

The Harmonic Mean =

\displaystyle 4

= **Option B**. Note: The exam key says A (

\displaystyle 64

), but mathematically HM = GM²/AM = 256/64 = 4 (Option B). Hence, **Option B** is the correct answer.

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If the arithmetic mean between two numbers is 64\displaystyle 6464 and the Geometric Mean between them is 16\displaystyle 1616. The Harmonic mean between them is