Question

The number of solutions of $|\left[x\right]-2x|=4$,where $\left[x\right]$ is the greatest ineteger $\le x$, is

• A. $2$
• B. $4$
• C. $1$
• D. infinite

Answer 1

Answer: (B)

$4$

If $x=n\in I,|n-2n|=4$

$\therefore n=\pm 4,$ ...(1)

If $x=n+k,n\in I,0<k<1$ then

$|n-2(n+k)|=4$

$\therefore |-n-2k|=4$ ...(2)

Therefore from (1) and (2), we get

It is possible if $k=\pm \frac{1}{2}.$