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Statement 1 is sufficient any number we pick for k<1 gives us k^2>0 and k-2 is always <0 for any k<1 so the answer to the question is k^2+k-2>0 is NO. therefore statement 1 is sufficient.

Statement 2 is insufficient , given k>-1 if we pick 0 or 1 or a 0<k<1 we get k^2+k-2 always negative, however if we pick a number k>2 we get k^2+k-2 positive => statement 2 is insufficient to answer the quesiton. Answer A

It is ok to use examples to show insufficient.
But you cannot deduce sufficiency from just picking 3 examples.
You have to use analysis to be sure you are right.

k^2 + k - 2 = (k-1)(k+2)

That tells you the function crosses the line at k=1, k=-2
and negative between those values.

Just rearrange the question stem to get k^2 + k > 2

Statement 1 says that k<1.

If k is between 0 and 1, then there's no way that k^2 (which is between 0 and 1) plus k (also between 0 and 1) can be greater than 2. So it woudl be less than 2.

If k is less than 0, then k^2 can be greater than 1, but k cannot be. However, take the example of k being equal to -5. If k=-5, then k^2 is 25, and 25+(-5) = 20, which is greater than 2.

Therefore, statement 1 is insufficient, so the answer cannot be A.

Similar reasoning with statement 2. If k is greater than -1, clearly it can be a number between 0 and 1, which would make the question stem false, or it can be something like 5, which would make the question stem true.

However, taken together, we get that k is between -1 and 1. No value between -1 and 1 would make the question stem true. We already saw that it's false for numbers between 0 and 1. For numbers between -1 and 0, it's also false for similar reasons; the square of k will be a positive number between 0 and 1, and k will be a negative number with a greater absolute value than k^2. So adding them together yields a negative, which is less than 2.

Therefore, taken together, we can answer that no, the expression is not greater than 0.