Question

The product of $n$ positive numbers is 1. Their sum is

• A. a positive integer
• B. divisible by $n$
• C. equal to $n+\frac{1}{n}$
• D. greater than or equal to $n$

Answer 1

The correct option is D greater than or equal to $n$

Let the numbers be $a_1,..,a_n$
For positive numbers,$AM\ge GM$
$\therefore \frac{a_1+a_2+.....+a_n}{n}\ge (a_1.a_2......a_n{)}^{\frac{1}{n}}=1$
$\Rightarrow a_1+a_2+.....+a_n\ge n$
Hence, option D is correct.