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Sample Worksheet: Algebraic Shortcuts for the SAT, GRE, GMAT

Most students taking the SAT, GRE, or GMAT know their algebra fairly well, but many find they can't complete all the problems in the allowed time. Why? It's NOT because those students are just naturally slow: it's because they're doing more work than they need to! It's not their speed but their very approach --- the very way they conceive of the process of problem-solving --- that's flawed. To ace the math sections of standardized tests, you have to learn how to attack problems in new ways so that you get the right answers by doing as little work as possible! (Part of the reason so many students don’t already know how to do this is that it’s not taught well throughout middle and high school math classes. Learning how to think quickly and deeply often requires UNLEARNING habits your math teachers instilled in you in school!)

To see if you’re up to par, try the following problems, which test your ability to make deep algebraic connections that will save you time. If your algebraic skills are what they really should be, you should be able to do all the problems in TWENTY SECONDS OR LESS! If you can’t, send me an email and start working with me today!


Suppose 2x+7=19. Find the value of each of the following expressions WITHOUT solving for x!

a) 4x+14
b) 6x+21
c) 20x+70
d) 2x+6
e) 2x+3
f) 2x
g) 2x-7
h) 2x-20
i) x+3.5
j) 0.5x+1.75
k) -2x-7
l) 10x+7
m) 8x+10