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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8228
GMAT 1: 760 Q51 V42 GPA: 3.82

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Difficulty:   35% (medium)

Question Stats: 61% (00:57) correct 39% (01:16) wrong based on 18 sessions

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If $$w^2 x^3 y^4 z^5 < 0$$, is $$xyz > 0$$?

1) $$x < 0$$

2) $$y < 0$$

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8228
GMAT 1: 760 Q51 V42 GPA: 3.82

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1
Official Solution:

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, and then recheck the question.

Modifying the original condition and question:

The original condition $$w^2 x^3 y^4 z^5 < 0$$ is equivalent to $$xz < 0$$ since we can ignore terms with even exponents in this type of inequality (they are always positive).

Under the modified condition $$xz < 0$$, the question, 'is $$xyz > 0$$?' is equivalent to 'is $$y < 0$$?', which is the same as condition 2).

Since condition 1) tells us nothing about the sign of y, the answer is B.

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Intern  B
Joined: 20 Nov 2018
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I think this is a high-quality question and I agree with explanation.
Intern  Joined: 23 May 2019
Posts: 3

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I think this is a poor-quality question. I do not understand how the answer to the question is B.
I know that given that the powers are even, the outcome will be positive. But, I do not know how to go from there.
Intern  B
Joined: 23 Feb 2019
Posts: 8

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tulullus wrote:
I think this is a poor-quality question. I do not understand how the answer to the question is B.
I know that given that the powers are even, the outcome will be positive. But, I do not know how to go from there.

I will try to explain:

Given the stem, we know that either x or y has to be less than 0, but not BOTH, as if both are less than 0, then the expression would result in >0, which violates what we are given.

So we are trying to solve whether xyz>0. We know given the stem, that x and z have opposite signs, therefore, we are needing to determine if y is greater to or less than 0. We don't know the sign of y, due to its having a positive exponent in the stem (could be positive or negative)

Statement 1: x<0 --> this would imply that z>0, but gives no info on y and is therefore INSUFFICIENT

Statement 2: y<0 --> we already know that x and z have opposite signs and now know that y is negative. Therefore we have (pos*neg*neg) which is >0 OR (neg*neg*pos) which is also > 0 SUFFICIENT Re: M60-09   [#permalink] 18 Jul 2019, 03:08
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# M60-09

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