Question

Let $x_1,x_2,.....,x_{15}$ be $15$ distinct numbers chosen from $1,2,3,.....,15$. Then the value of $(x_1-1)(x_2-1),(x_3-1)....(x_{15}-1)$ is

• A. $Always\le 0$
• B. $0\left(zero\right)$
• C. Always even
• D. Always odd

Answer 1

Answer: (B)

$0\left(zero\right)$

Among $x_1,x_2,x_3,....,x_{15}$; one of them, say, $x_k$ is $1$.
$\Rightarrow x_k-1=0\Rightarrow$ the product given is $0$