IPMAT Indore 2023 (MCQ) - Let [x] denote the greatest integer not exceeding x and x = x - [x] If n is a natural number, then the sum of all values of x satisfying the equation 2[x] = x + nx is | PYQs + Solutions

IPMAT Indore 2023

Number System

Integral Solutions

Medium

Let $[x]$ denote the greatest integer not exceeding $x$ and { $x$ } $= x - [x]$ If $n$ is a natural number, then the sum of all values of $x$ satisfying the equation $2[x] = x + n$ { $x$ } is

\dfrac{n(n+2)}{2}

\dfrac{3}{2}

\dfrac{n(n+1)}{2}

n

Correct Option: 1