Question

For how many positive integer values of $n$ will the value of the expression $2n^2+1$ be an integer greater than $2$ and smaller than $400$?

• A. $18$
• B. $32$
• C. $28$
• D. $14$

Answer 1

The correct option is D $14$

Solve the inequality:

$2<2n^2+1<400$

$2-1<2n^2+1-1<400-1$

$\left(\frac{1}{2}\right)<n^2<\left(\frac{399}{2}\right)$

Since $n$ is positive

$\sqrt{\left(\frac{1}{2}\right)}<n<\sqrt{\left(\frac{399}{2}\right)}$

Since $n$ is an integer

$1\le n\le 14$

The number of integers between $1$ and $14$ inclusive is $14$.