The inflation rate of a country follows a certain trend given by $I = I_{X} + I_{X - 1} + I_{X - 2}$ where $[I_{X}] = 0, [I_{X - 1}] = 1$ and $[I_{X - 2}] = 2$ , [ ] represents greatest integer function. Find the range of the inflation rate.

[3, 6)

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[0, 3)

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[1, 3]

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Cannot be determined

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Solution

The correct option is A
[3, 6)

$[I_{X}] = 0 \Rightarrow 0 \leq I_{X} < 1$ ----- (i)

$[I_{X - 1}] = 1 \Rightarrow 1 \leq I_{X - 1} < 2$ ----(ii)

$[I_{X - 2}] = 2 \Rightarrow 2 \leq I_{X - 2} < 3$ ----(iii)

Adding (i), (ii) & (iii), we get,

$3 \leq [I_{X}] + [I_{X - 1}] + [I_{X - 2}] < 6$

$3 \leq I < 6 \leq I ϵ [3, 6) .$

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