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From (1), if t > 0, then t will have values 1,2,3... and -t will have values -1,-2,-3...
But we do not have a range for r. r could be having values 0,1,2,3,4... in which case it satisfies the equation
Conversely, r could be -3 when t is -2 and so smaller than -t
Therefore (1) is not sufficient.
From (2), we are told r > 0, so we know for sure it is bigger than any negative value and satisfies the equation.
And when we satisfy (r+t)/(r-t)>0, we will know r > t because if this isn't so, (r+t)/(r-t) may be < 0.