First translate the question into math on your paper.
w>1 ?
Then look at Statement 1 alone, which says
w+2>0
We can manipulate inequalities just as we do with algebra, for the most part. You run into one exception when you need to divide or multiply by a negative. When you do so, you must flip the sign. Luckily, we don't need to do that here. The question is asking about w, so we want to see what this statement tells us about w. Subtract two from each side to isolate w.
w>-2
Because this is a Yes/No question (as opposed to a value question), we can prove the statement insufficient by finding a YES case and a NO case.
YES case: w = 4
NO case: w = 0
Note that both cases above satisfy the condition of Statement 1, but they give opposing answers to the original question. When testing cases, however, we must always remember that the statements are always true.
INSUFFICIENT
Statement 2: w^2>1
Again, our goal is going to be to find a YES case and a NO case. There are at least two possible methods here:
Method 1: Draw a number line to help you visualize possibilities. Test numbers along the number line to find the limits of this condition. You will find that w must be greater than 1 or less than -1.
Method 2: For the more algebraically inclined, you may take the square root of both sides, but you'll have to end up with the absolute value of w, rather than just w.
|w|>1
This tells you that w is more than 1 away from 0. In other words, it is greater than 1 or less than -1.
YES case: w = 5
NO case: w = -5
INSUFFICIENT
Statements 1 + 2 combined gives us the following:
w>1 OR -2<w<-1
Because the question never told us w was an integer, we cannot assume it is one.
YES case: w = 5
No case: w = -1.5
INSUFFICIENT
The correct answer is E.
