GMAT Question of the Day - Data Sufficiency - Absolute Value/Number Properties
If a and b are non-zero numbers is |a|/b < 1?
(1) |a| + b < a + |b|
(2) |a| - |b| < 0
GMAT Question of the Day - Data Sufficiency - Solution
This is a tough GMAT question but if you stay organized you should be able to get through it. Take this one (careful) step at a time. Don't make any assumptions. Avoid careless mistakes as they compound and make GMAT questions seem far more difficult than they are. Also, always consider that there may be an easier way of doing things. In data sufficiency always keep number properties in mind.
Statement (1) This is absolute value so let's think in the context of positive/negative. If a is positive then somehow the b on the left hand side must decrease that sides value so it is less than the right hand side. So b must be negative. If a is negative then be must be a greater negative to balance out a's negativity. So we have two possibilities:
1: a > 0 and b < 0
2: a < 0 and b < 0 and b < a
Either of these will produce a negative value for |a|/b because the signs will always be opposite. Sufficient.
Statement (2) |a| < |b| this will always produce a value for |a|/b that is less than one regardless of the signs. It will either be a negative number or a fraction between 1 and 0. Sufficient.