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

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

by Max@Math Revolution » Thu Jan 18, 2018 12:36 am
[GMAT math practice question]

$$If\ w^2x^3y^4z^5<0,is\ xyz>0?$$
1) x<0
2) y<0
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jan 18, 2018 4:03 am
Max@Math Revolution wrote:[GMAT math practice question]

$$If\ w^2x^3y^4z^5<0,is\ xyz>0?$$
1) x<0
2) y<0
w²x³y�z�<0 implies that w, x, y and z are all NONZERO, with the result that any even power of w, x, y and z will be POSITIVE.
Thus, we can safely divide w²x³y�z�<0 by any even power of w, x, y and z:
(w²x³y�z�)/(w²x²y�z�) < 0/(w²x²y�z�)
xz < 0.

Since xz<0, xyz>0 only if y is NEGATIVE.
Question stem, rephrased:
Is y<0?

Statement 1:
No information about y.
INSUFFICIENT.

Statement 2.
SUFFICIENT.

The correct answer is B.
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by Max@Math Revolution » Sun Jan 21, 2018 5:30 pm
=>

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^2x^3y^4z^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.

Therefore, the answer is B.
Answer: B
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