If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [ ( p + q ) s ] + r?

Answer: Option B

56 × 75 × 60 × 84 × 210 = 2^p × 3^q × 5^r × 7^s
7 × 2³ × 5² × 3 × 2² × 3 × 5 × 2² × 3 × 7 × 7 × 3 × 2 × 5 = 2^p × 3^q × 5^r × 7^s
2⁸ × 3⁴ × 5⁴ × 7³ = 2^p × 3^q × 5^r × 7^s
∴ p = 8
q = 4
r = 4
s = 3
$$\begin{array}{rl}& \therefore \left[\frac{\left(\text{p}+\text{q}\right)}{\text{s}}\right]+\text{r}\\ & =\left[\frac{\left(8+4\right)}{3}\right]+4\\ & =\frac{12}{3}+4\\ & =4+4\\ & =8\end{array}$$