If $y = 3 [x] + 1 = [x - 1] - 10$ , where [ ] represents greatest integer function, then $[x + 2 y]$ is

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Solution

The correct option is C $- 40$
$[x - 1] = [x] - 1$

$3 [x] + 1 = [x] - 1 - 10$

$\Rightarrow 2 [x] = - 12$

$\Rightarrow [x] = - 6$

Also $y = 3 [x] + 1 = - 18 + 1 = - 17$

$- 6 \leq x < - 5$

Hence $- 6 + 2 y \leq x + 2 y < - 5 + 2 y$

$- 40 \leq x + 2 y < - 39$

Hence $[x + 2 y] = - 40$

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