If a and b are consecutive negative integers, is a less than b ?
(1) a + 1 and b - 1 are consecutive negative integers.
(2) a is an odd integer.
\(a\) and \(b\) are consecutive integers means that either:
\(b=a+1\) (for example \(a=-5\) and \(b=-4\)), in this case \(a<b\);
\(a=b+1\) (for example \(a=-5\) and \(b=-6\)), in this case \(a>b\).
So the we should determine which case we have.
(1) \(a+1\) and \(b-1\)are consecutive negative integers --> again either \(a+1=b-1+1\) --> \(a+1=b\) (first case so \(a<b\)) or \(b-1=a+1+1\) --> \(b=a+3\), which is not possible as \(a\) and \(b\) are consecutive integers (difference between two consecutive integers can not equal to 3). Sufficient.
(2) \(a\) is an odd integer. Clearly insufficient.