Question

Given $f\left(x\right)=\left[\frac{1}{3}+\frac{x}{66}\right]$, then $\sum _{x=1}^{66}f\left(x\right)$ is

• A. $21$
• B. $23$
• C. $30$
• D. $66$

Answer 1

Answer: (B)

$23$

$f\left(x\right)=[\frac{1}{3}+\frac{x}{66}][.]$ is greatest integral function

$f\left(x\right)=0$ from $x=1$ to $43$

$f\left(x\right)=1$ from $x=44$ to $66$

$\sum _{x=1}^{66}f\left(x\right)=\sum _{x=1}^{43}0+\sum _{x=44}^{66}1$

$=23$

$B$ is correct.