Another question that I love and that plays with students’ tendency to apply what they have learned sort of automatically and uncritically is the following GMAT question. I have done this one with SAT/ACT/GMAT students alike and almost everyone begins by factoring the quadratic. It’s one of my favorite questions and it really teaches people to “think before they do.”
If (4-x) / (2+x) = x, what is the value of x^2 + 3x - 4?
And although the discussion about Math on the new SAT is in another post, I must also bemoan the fact that the above type of question will be less likely to appear on the new test. Boo hoo.