For what value of * the statement ( *15 ) ( *135 ) = 1 is true ?

Answer: Option D

$$\begin{array}{rl}& \text{Method 1:}\\ & \text{Let the missing number be }x\\ & \text{Then, }\\ & \iff x^2=15\times 135\\ & \iff x=\sqrt{15\times \left(15\times 9\right)}\\ & \iff x=\sqrt{{15}^2\times 3^2}\\ & \iff x=15\times 3\\ & \iff x=45\\ & \\ & \text{Method 2:}\\ & \text{Let the missing number be }x\\ & \text{Then, }\\ & \iff x^2=15\times 135\\ & \iff x^2=2025\\ & \iff x=\sqrt{2025}\\ & \iff x=45\end{array}$$