If xyz ≠0, is x^3y^4z^5 > 0?

[Max@Math Revolution]

[GMAT math practice question]

If xyz ≠ 0, is x^3y^4z^5 > 0?

1) xz > 0
2) xyz > 0

[Brent@GMATPrepNow]

If xyz ≠ 0, is x³y�z� > 0?

1) xz > 0
2) xyz > 0

Given: xyz ≠ 0

Target question: Is x³y�z� > 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 x³y�z� > 0 and divide both sides by x² to get: xy�z� > 0
Similarly, since y� is POSITIVE, we can safely divide both sides by y� to get: xz� > 0
Finally, since z� is POSITIVE, we can safely divide both sides by z� to get: xz > 0
REPHRASED target question: Is xz > 0?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?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

Answer: A

Cheers,
Brent

[Max@Math Revolution]

=>

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.

Therefore, A is the answer.
Answer: A