Hi, 
You're right in your conclusion that when a<b; upon adding 7 to the numerator and denominator, the new fraction will be greater than the original one; and if a>b, upon adding 7 to the numerator and denominator, the new fraction will be lesser than the original one. 
However, the question asks which of the statements can be regarded as redundant. 
Statement I: Gives us clear values and we can see that it can give a clear answer. 
Statement II: Says, essentially that a<b; But this need not always satisfy the answer. 
Let's see two cases, a= -7 and b=3, in this case adding 7 will give a new fraction of 0, which is greater than the original fraction. 
Meanwhile if we take a= -9 and b= -7, in this case the fraction will be 9/7 which upon adding 7 will change to 16/14 or 8/7, which is less than the original fraction. 
Statement III: Also essentially say that a>b 
There two we can take negative values of one or both of the variables to see that this too does not conclusively give a definite answer. 
Therefore, of all the given statements I is the most accurate and definite source of answers and the others can be dispensed with.
Hope this would have cleared your doubt. 
Please feel free to ask any further questions you might have. 
Regards