1. Use the Arrhenius equation for each step:

$k_i = A_i e^{-E_i/(RT)}$

where $E_i$ is the activation energy of step $i$.

2. Given:

$k = \sqrt{\frac{k_1 k_3}{k_2}}$

Substitute the Arrhenius forms:

$k = \sqrt{\frac{A_1 e^{-E_1/(RT)} \cdot A_3 e^{-E_3/(RT)}}{A_2 e^{-E_2/(RT)}}}$

$k = \sqrt{\frac{A_1A_3}{A_2} \; e^{-(E_1+E_3-E_2)/(RT)}}$

3. Take the square root:

$k = \left(\frac{A_1A_3}{A_2}\right)^{1/2} e^{-\frac{E_1+E_3-E_2}{2RT}}$

Compare with Arrhenius form:

$k = A e^{-E_{\text{overall}}/(RT)}$

So,

$E_{\text{overall}} = \frac{E_1 + E_3 - E_2}{2}$

4. Substitute the given activation energies:

$E_1 = 60, \quad E_2 = 30, \quad E_3 = 10 \quad (\text{kJ mol}^{-1})$

$E_{\text{overall}} = \frac{60 + 10 - 30}{2} = \frac{40}{2} = 20 \text{ kJ mol}^{-1}$

5. Nearest integer:

$\boxed{20}$

Comparison with stored correct answer:

Stored correct answer = $20$. This matches the derived answer.