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KVPY2015MathematicsFunctions

For a real number x , let [x] denote the largest integer less than or equal to x , and let x =x-[x] . The number of solutions x to be equation [x] x =5 with 0 x 2015 is

Options

  1. A0
  2. B3
  3. C2008
  4. D2009

Correct answer

D. 2009

Step-by-step solution

array l x =x-[x] [x] x =5 f 0 I f=5 0 < f < 1 array Possible solutions (6+ 5 6 ), (7+ 5 7 ), ., (2014+ 5 2014 )=2009

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