If $[x]$ denotes the greatest integer less than or equal to $x$ for any number $x,$ is $[a]+ [b]=1?$

If $[x]$ denotes the greatest integer less than or equal to $x$ for any number $x,$ is $[a]+[ b ] = 1?$

(1) $ab=2.$

(2) $0 < a < b < 2.$

Answer: A

Source: GMAT Club Tests

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