If 0 x x ] is the greatest integer less than or equal to x, the number of possible values…

Mathematics · JEE Advanced · NTA ExamsSets, Relations and Functions

If 0 < x < 1000 and \(\left[\frac{x}{2}\right]+\left[\frac{x}{3}\right]+\left[\frac{x}{5}\right]=\frac{31}{30} x\), where [x] is the greatest integer less than or equal to x, the number of possible values of x is
  1. 34
  2. 32
  3. 33
  4. none of these

Answer

(C) 33

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