Question

For a real number $x$, let $\left[x\right]$ denote the largest integer less than or equal to $x$, and let $\left\{x\right\}=x-\left[x\right]$. The number of solution $x$ to be equation $\left[x\right]\left\{x\right\}=5$ with $0\le x\le 2015$ is.

• A. $0$
• B. $3$
• C. $2008$
• D. $2009$

Answer 1

The correct option is D $2009$

$\left\{x\right\}=x-\left[x\right]$
$\left[x\right]\left\{x\right\}=5f\ne 0$
$If=5$
$0<f<1$
Possible solutions
$(6+\frac{5}{6}),(7+\frac{5}{7}),.....,(2014+\frac{5}{2014})=2009$.