How many different positive integral values, less than 1000, y = x[x] can take where x is a positive real number.

Note:- [x] is greatest integer less than or equal to x
For eg.  [3.5] = 3, as 3 is the largest integer less than or equal to 3.5
Similarly [4] = 4, [3.99] = 3
1. 31
2. 496
3. 30
4. None of these

If [x] = k (an integer), then
x can be k, k + 1/k, k + 2/k, ……, k + (k – 1)/k

So, for every integer k, we will have k values

Now, k can not be 32, as then the lest value of y will be 1024

So, answer will be 1 + 2 + 3 + … + 31 = 496