Question

Let $x_{1}, x_{2}, ............ ,x_{15}$ be 15 distinct numbers chosen from $1, 2, 3,........... , 15.$ Then the value of $\left(x_{1}-1\right),\left(x_{3}-1\right) .......... \left(x_{15}-1\right)$ is

• A. always $\le 0$
• B. $0$ (zero)
• C. always even
• D. always odd

Answer 1

Answer: (B)

Since, $x_{1}, x_{2}, \ldots, x_{15}$ are among $1,2,3, \ldots, 15 .$ So, $x_{1}$ can take any value from $1,2,3, \ldots$, 15. Among these values, one of the number must be 1 , hence product will be 0 .