Question

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 is 0 $\le$ x $\le$ 2015 is

• A. 0
• B. 3
• C. 2008
• D. 2009

Answer 1

The correct option is D

2009

{x} = x - [x]

[x]{x} = 5 f $\ne$ 0

If = 5

0 $<$ f $<$ 1

Possible solutions

$(6+\frac{5}{6}),(7+\frac{5}{7}).......,(2014+\frac{5}{2014})=2009$