Question

If $\left[x\right]\le n\forall n\in Z.$ Then choose the possible value(s) of $n$ for which $x=\mathrm{6.6.}$ Where $[.]$ denotes GIF.

• A. $6$
• B. $5.6$
• C. $-6$
• D. $7$

Answer 1

Answer: (A), (D)

$7$

As we know that if $\left[x\right]\le n\Rightarrow x<n+1\forall n\in Z.$

$\Rightarrow n+1>x$
$\Rightarrow n>x-1$

Substituting $x=6.6,$ we get:
$\Rightarrow n>6.6-1$
$\Rightarrow n>5.6$

Thus, $n$ can be any integer greater than $\mathrm{5.6.}$
From the given options, $6$ and $7$ are the possible values.