Question

If $y=2\left[x\right]+30,y=3[x-2]+15$, then $[x+y]$ is equal to
(where [.] denotes greatest integer function)

• A. $93$
• B. $72$
• C. $52$
• D. $94$

Answer 1

The correct option is A $93$

$y=3[x-2]+15\Rightarrow y=3\left[x\right]-6+15$
$(\because [x+I]=\left[x\right]+I,\forall I\in Z)$

Now,
$2\left[x\right]+30=3\left[x\right]+9$
$\Rightarrow 21=\left[x\right]$
$\Rightarrow y=2\left(21\right)+30=72$

$\therefore [x+y]=\left[x\right]+y=21+72=93$