If and , where is the greatest integer less than or equal to , then the number of…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

0<x<1000

and

\left\lfloor\frac{x}{2}\right\rfloor+\left\lfloor\frac{x}{3}\right\rfloor+\left\lfloor\frac{x}{5}\right\rfloor=\frac{31}{30}x

, where

\lfloor x\rfloor

is the greatest integer less than or equal to

x

, then the number of possible values of

x

is (1) 32 (2) 33 (3) 34 (4) None of these