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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If xyz ≠ 0, is x^3y^4z^5 > 0? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If xyz ≠ 0, is x^3y^4z^5 > 0? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] If xyz ≠ 0, is x^3y^4z^5 > 0? 1) xz > 0 2) xyz > 0 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
If xyz ≠ 0, is x³y⁴z⁵ > 0?

1) xz > 0
2) xyz > 0
Given: xyz ≠ 0

Target question: Is x³y⁴z⁵ > 0?
This is a great candidate for rephrasing the target question.
Since we know that x² must be POSITIVE, we can safely take the inequality x³y⁴z⁵ > 0 and divide both sides by x² to get: xy⁴z⁵ > 0
Similarly, since y⁴ is POSITIVE, we can safely divide both sides by y⁴ to get: xz⁵ > 0
Finally, since z⁴ is POSITIVE, we can safely divide both sides by z⁴ to get: xz > 0
REPHRASED target question: Is xz > 0?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: xz > 0
PERFECT!
The answer to the REPHRASED target question is YES, xz IS greater than 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: xyz > 0
There are several values of x, y and z that satisfy statement 2. Here are two:
Case a: x = 1, y = 1 and z = 1. In this case, xz = (1)(1) = 1. So, the answer to the REPHRASED target question is YES, xz IS greater than 0
Case b: x = 1, y = -1 and z = -1. In this case, xz = (1)(-1) = -1. So, the answer to the REPHRASED target question is NO, xz is NOT greater than 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Asking if x^3y^4z^5 > 0 is equivalent to asking if xz > 0 since we can ignore even exponents in inequalities.
Thus, condition 1) is sufficient.

Condition 2)
If x = 1, y = 1 and z = 1, then x^3y^4z^5 > 0, and the answer is “yes”.
If x = 1, y = -1 and z = -1, then x^3y^4z^5 < 0, and the answer is “no”.
Condition 2) is not sufficient since it does not yield a unique answer.

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