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St 1 :
if a is a +ve number. mod. b > mod. a
But if a is a -ve number ...-a will be positive
so b< -a can be any number less than the positive integer -a ..i.e can be number between -a and +a and also beyond +a (i.e -ve ) ...so mod b can be less than or greater than mod a .

st 2 ..by itself isn't enough

Combining 1,2 ----Gives only that a is -ve..the exact range in which b lies viz., if it is between 0 and a (-ve value ) or is still lesser than a .