Hi jjjinapinch,

We're asked if X is less than 5. This is a YES/NO question. We can answer this question by TESTing VALUES and paying careful attention to the question that is asked. To start, we know that ANY negative value for X and X=0 will lead to a YES answer (as well as any values of X that are less than 5). Answers that are 5 or greater will lead to a NO answer.

1) X² > 5

With this inequality, there are clearly multiple values for X (positive and negative).
IF... X = 5, then the answer to the question is NO.
IF... X = -5, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X² + X < 5

With this inequality, we know that there are negative solutions and that X=0 is a solution, so there are clearly "NO" answers to this question. However, we now have to think about how big X could get. Thankfully, there's a way to avoid doing that exact math and use a bit of 'brute force' to help us to stop working...

IF.... X=1, then (X^2 + X) = 1^2 + 1 = 2... which is less than 5
IF.... X=2, then (X^2 + X) = 2^2 + 2 = 6... which is GREATER than 5
As X increases, the sum of (X^2 + X) will also increase. Since we're already greater than 5 when X=2, there's no reason to check any larger values. Given this inequality, X MUST be less than 2, so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

jjjinapinch wrote:Is x < 5?
(1) x^2 > 5
(2) x^2 + x < 5

We need to determine whether x < 5.

Statement One Alone:

x^2 > 5

If x = 3, then x is less than 5. However, if x = 6, then x is not less than 5. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x^2 + x < 5

Thus, we have x < 5 - x^2. Since x^2 is nonnegative, we have 5 - x^2 ≤ 5. Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5.

Answer: B