Question

Number of real roots of the equation $6x-7[x]=2$ is
[Note: $[k]$ denotes greatest integer function less than or equal to $k$.]

• A. 6
• B. 5
• C. 8
• D. 7

Answer 1

Answer: (A)

$6\{x\}=2+[x]$
$0\le \{x\}=\frac{1}{3}+\frac{[x]}{6}<1$
$-2\le [x]<4$
$\Rightarrow [x]=-2,-1,0,1,2,3$
$\{x\}=0,\frac{1}{6},\frac{1}{3},\frac{1}{2},\frac{2}{3},\frac{5}{6}$