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 Author: questioner [ Sun Oct 09, 2011 1:43 pm ] Post subject: GMAT Algebra (Data Sufficiency) Is k² + k – 2 > 0?(1) k is an integer greater than zero.(2) k divided by 2 is an integer.A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.D. Either statement BY ITSELF is sufficient to answer the question.E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.(C) The first thing we need to do is factor k² + k – 2 into (k + 2)(k – 1). From these factors, we can see that the value of k² + k – 2 = 0 when k = -2 or 1.When k > 1, both k + 2 and k – 1 will be positive, so the product of the two (the original expression) will be positive.Similarly, when k is between -2 and 1, the product of the two expressions will be negative.Finally, when k is less than -2, the product will be positive.So we've learned that k² + k – 2 > 0 as long as k is greater than 1 or less than -2.Statement (1) tells us that k is an integer greater than zero. This is not sufficient because k² + k – 2 > 0 when k is greater than 1, but it will equal zero when k is 1.Statement (2) tells us k is an even integer. This is also insufficient, because all even integer values of k will make k² + k – 2 greater than zero except -2 and 0. k = -2 will make the expression equal to zero, and k = 0 will make the expression negative. (Remember: 0 is an even integer!)Combined, the two statements are sufficient, because the only possible values for k are positive even numbers (2 or greater), all of which make k² + k – 2 > 0.Since the statements are insufficient individually, but sufficient when combined, the correct answer is choice (C).----------This question doesnt make any sense with your explanation.

Author:  Gennadiy [ Sun Oct 09, 2011 1:53 pm ]
Post subject:  Re: GMAT Algebra (Data Sufficiency)

Quote:
This question doesnt make any sense with your explanation.
What exactly don't you understand?

Here are the key moments for your consideration:
1. We solve the inequality. The solution can be displayed as:

2. We try statement (1). It is NOT sufficient, because k² + k – 2 can be positive, but it can be zero as well (if k = 1). We have two different answers to the main question, so it is NOT sufficient.

3. We try statement (2). It is NOT sufficient, because k² + k – 2 can be positive, negative or 0.

4. The both statements combined define k to be a positive even integer (2, 4, 6 ....). All this values make k² + k – 2 to be positive. So the answer to our main question is always "YES". Therefore the both statements combined are sufficient to answer the question.