bomond wrote:There is one way if you want. But it's a bit odd.
ST 1. In order to avoid model square(sorry can't express) the both sides
(x+1)^2=(2(x-1))^2
x^2+2x+1=4x^2-8x-4
Math is a bit off:
(x+1)^2=(2(x-1))^2
x^2 + 2x + 1 = (2x - 2)^2
x^2 + 2x + 1 = 4(x^2) - 8x
+ 4
0 = 3(x^2) - 10x + 3
0 = (3x - 1) (x - 3)
3x = 1 or x = 3
x = 1/3 or x = 3
x may or may not be between -1 and +1.. insufficient.
However, when we combine with:
(2) x ≠ 3
we know that the only possible value of x is 1/3, so choose (c): together the statements are sufficient.
In fact, (c) is a great strategic guess on this question, long before doing all the math.
Statement (2) seems pretty random, so either we're being given a totally useless piece of information or x ≠ 3 will eliminate a possibility from (1). As soon as we see that (1) can be turned into a quadratic, we should anticipate that (1) will give us two values for x (so will be insufficient) and (2) will narrow it down to just one possibility.
The better you know the GMAT, the less work you'll need to do to confidently pick up points. Knowing how and when to guess strategically is a huge advantage on test day.
To go back to the original poster's question, yes, squaring both sides of an absolute value equation is often a great approach to these questions.
