Question

If $n$ is the smallest natural number such that $n+2n+3n+.....+99n$ is a perfect square, then the number of digits in $n^2$ is

• A. $1$
• B. $2$
• C. $3$
• D. More than $3$

Answer 1

Answer: (C)

$3$

$n+2n+3n+......+99n$
$n(1+2+3+..........+99)$
$n\frac{\left(99\right)\left(100\right)}{2}=9\times 25\times 22\times n$ is a perfect square when $n=22$
Number of digits in $n=3$