What is the distance between a and b on the number line?
(1) |a| – |b| = 6
(2) ab > 0
From F.S 1, let's pick values keeping |a| – |b| = 6. For a=-12; b=6, we have |a-b| = 18, however, for a=12;b=6 we have |a-b| = 6. Insufficient.
From F.S 2, we just know that a and b are of the same sign. Insufficient.
With both taken together, either a,b>0 in which case, |a| – |b| = 6 --> a– b = 6 .
a,b<0 in which case, b-a = 6. Thus, the distance between the points a and b, |a-b| is the same in either case. Sufficient.
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions