Inequalities

A couple of hacks to get done with Inequalities problems on the GMAT quickly. These might not help you to solve the entire problem. However, these can help you to reduce the amount of time spent in evaluating answer choice, specifically for DS questions.

|x-5| < 2

How do we interpret the above (in)equation? The normal/longer root would be to solve for two equations - one treating the outcome of (x-5) as positive and another treating the outcome of (x-5) as negative. Thus the two equations you would solve would be for (x-5) = 2 and (x-5)= -2 and then finally, replace the "=" with a "<".

A shorter, easier, less error prone method would be to rephrase the (in)equation - read it as x is less than 2 units away from 5. Reading it this way, the answer instantly pops out that x can take values from 3 to 7

Original inequation	Rephrasing	Range of x
|x+5| < 2	x is less than 2 units away from -5	from -7 to -3
|x+5| < 2	x is greater than 2 units away from -5	from -inf to -7 and -3 to +inf