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 Post subject: GMAT Algebra (Data Sufficiency)
PostPosted: Sat May 01, 2010 12:05 pm 
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Is (x – 2)(x – 5)(x + 2) > 0?
(1) x = 2
(2) x = 0

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF issufficient 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.

(D) Either statement gives us definite value for x. So using any statement we can calculate (x – 2)(x – 5)(x + 2) and tell if the value we get is greater than 0 or not. The
right answer is (D).

------------------------

I am slightly confused here. using x = 2 from the first statement, we get 0 = 0 as the answer, which is not greater than 0 but is equal to zero. The second statement provides us with a positive answer greater than zero. If the questions was "is (x - 2)(x - 5)(x + 2) ≥ 0" then I believe the answer would be D. Am I missing something here?


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 Post subject: Re: Math:test 4, question 17 (Data sufficiency: basic principle)
PostPosted: Sat May 01, 2010 12:34 pm 
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In data sufficiency questions statement (or statements) is sufficient if we can give a definite answer to the main question of a problem. The main term here is DEFINITE. It can be some value (number, name, etc.), "Yes", or "No". Note, that negative answer is also a definite answer.

In this specific question, using statement (1) we can calculate:

(x – 2)(x – 5)(x + 2) = (2 – 2)(2 – 5)(2 + 2) = 0

So we have a definite answer for question "Is (x – 2)(x – 5)(x + 2) > 0?" we definitely can state: No, it is not. We got a negative definite answer, so statement (1) by itself is sufficient.

Using statement (2) we can calculate:

(x – 2)(x – 5)(x + 2) = (0 – 2)(0 – 5)(0 + 2) = 20

So we have a definite answer for question "Is (x – 2)(x – 5)(x + 2) > 0?" we definitely can state: Yes, it is. We got a positive definite answer, so statement (2) by itself is sufficient.

Either statement BY ITSELF is sufficient to answer the question. So the answer is (D).


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