Question

If $5$ and $2$ are the Arithmetic Mean and Harmonic Mean of two distinct numbers, then their Geometric Mean is

• A. $3$
• B. $7$
• C. $\sqrt{10}$
• D. $10$

Answer 1

The correct option is C $\sqrt{10}$

Given,

AM of two numbers $=5$, HM of two numbers $=2$.

By using the formula,

AM$\times$HM$=$GM${}^2$

$⟹$ $5\times 2=$GM${}^2$

$⟹$ GM${}^2=10$

$⟹$ GM$=\sqrt{10}$.

Hence, option C is correct.