Let z=[y] and y=[x]-x where [] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what is the value of z?

Explanation

Let x = 1.5. Then y = [1.5] - 1.5 = 1 - 1.5 = -0.5. Then z = [-0.5] = -1. In general, for any non-integer x, [x] - x gives the negative of the fractional part, which lies strictly between -1 and 0. The greatest integer of any number in this range is always -1.

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