Many of my students preparing for the SAT, GRE, and GMAT have decent algebraic intuition when it comes to EQUATIONS, but most are much weaker when it comes to INEQUALITIES.
On the one hand, this is entirely natural: inequalities capture less information than equations -- they establish merely a relation between two quantities, rather than their equivalence -- so they are inherently trickier to think about. But on the other hand, it's crucial to have a very solid grasp of how inequalities work to do well on the SAT, GRE, and especially the GMAT (which tends to love data sufficiency questions that deal with tricky inequalities).
To test yourself to see how up-to-speed you are, try to decide whether the following statements are true or false. (I have intentionally made the problems very abstract and seemingly confusing to see if you really know what's going on, so DON'T WORRY IF YOU'RE TOTALLY LOST OR INTIMIDATED!)
1. If a+b=c+d and e+f=g+h, then a+b+e+f=c+d+g+h.
2. If a+b=c+d and e+f=g+h, then a+b-e-f=c+d-g-h.
3. If a is less than b and c is less than d, then a+c is less than b+d. (WyzAnt won't let me use the greater and less than symbols on this blog!)
4. If a is less than b and c is less than d, then a-c is less than b-d.
Here's a hint -- one and only one of these statements is false! Do you know which one it is? The amazing thing is that although these problems LOOK scary, they are extremely simple if you know the basic rules for handling equations and inequalities.
To find out which one is false, send me an email & start preparing to ace the SAT, GRE, or GMAT today!