If a and b are integers, and |a| > |b|, is a · |b| < a – b?

[najibeltecle]

I get confused when i try to solve this question:

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab 0

The solution provided by MGMAT seems time consuming, it is based on exhaustive trials of all the possible scenarios.
I would like to know if there is another method to use when approaching problems with absolute values??

thank you

[mschwrtz]

could you rewrite S2? can't answer in the current form.