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If [ ] represents the greatest integer less than or equal to the given real number, and -1 ≤ x < 0, 0 ≤ y < 1, 1 ≤ z < 2, then the determinant [x] [y] [z] [x+1] [y+1] [z] [x] [y] [z]+1 is equal to:

1. [z]
2. [y]
3. [x]
4. None of these

Correct answer: [x]

Solution

With -1<=x<0, 0<=y<1, 1<=z<2: [x]=-1, [y]=0, [z]=1, [x+1]=0, [y+1]=1. The determinant of [[-1,0,1],[0,1,1],[-1,0,2]] expands to -1, which equals [x].

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