GMAT Question of the Day - Data Sufficiency - Absolute Value
Is x > 0?
(1) 3x - 2 = |3-x|
(2) x^2 > 1
GMAT Question of the Day Solution
Most GMAT tutoring students don't appreciate absolute value questions. Especially in the Data Sufficiency. That's understandable because GMAT absolute value questions can be tricky, especially if you don't approach them in an organized fashion. So how should you think about them? Whenever you see an absolute value question think about the signs (positive/negative). Think about what happens when the number in the absolute is positive and what happens when the number is negative. Also remember that an absolute value can't be negative. In a general sense that's all you have to worry about.
In this case we want to know if x is positive. If we're thinking in positive and negative we should see that the right side of the equation must be greater than or equal to zero (because it is an absolute value). So you can re-write the equation 3x - 2 is greater than or equal to 0. Solve and you will see that x must be positive. Sufficient. Statement (2) doesn't help us decide. You can pick and positive/negative value for x. This statement is just there for someone who doesn't understand the question and so might consider going for a seemingly safe "c" choice. Insufficient.