Of-late, I am doing Quant. questions in a different style - May be it will be of some use to you all.
When I see a question,I do not jump to solve -
Pause a moment (say 5-30 secs depending on problem and person)
1) Dissect the question in my mind
2) Think of the best way to solve the problem with least effort
3) Go for the solution
Believe me I have ended up not writing down in many cases.
Let me take an example from the question posted in Dana's post
Which of the following describes all values of x for which 1 - x^2 ≥ 0?
A. x ≥ 1
B. x ≤ -1
C. 0 ≤ x ≤1
D. x ≤ -1 or x ≥ 1
E. -1 ≤ x ≤ 1
This is an easy one. Most test-takers will not hesitate in solving it algebraically, but here goes: for A, pick x = 2: x^2 = 4 and 1 - 4 = -3, which is definitely smaller than 0. For B, pick -2 with the same results. Since D can be eliminated on the same examples, you're basically left with two choices: C and E. Here's where your real skills kick in: you know that the square of an integer is also the square of the integer's opposite. This means that, if a certain a is in the interval that you're looking for, -a will also be in there. So that means that choice E is indeed your answer.
Which of the following describes all values of x for which 1 - x^2 ≥ 0?
I pause a moment -
See that question is asking 1-some positive int ≥ 0
This will be possible only if that positive integer is between 0 and 1
again I see that positive integer is a square
So it can be between -1 and 1
I got the solution without writing down anything and the whole process took hardly 20 secs.
Again if nothing clicks in those 5-30 secs you can definitely go for the traditional/back-substituting way.
