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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 ## Is x/y^3>0? tagged by: Max@Math Revolution ##### This topic has 1 expert reply and 1 member reply ### GMAT/MBA Expert ## Is x/y^3>0? [GMAT math practice question] $$Is\ \frac{x}{y^3}>0?$$ $$\left(1\right)\ x-y\ >\ 0$$ $$\left(2\right)\ xy\ >\ 0$$ _________________ 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$99 for 3 month Online Course
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I would solve it like this:

the sign of y is the same of y^3. Hence, the question is the same as $$\text{Is}\ \ \frac{x}{y}>0\ ?$$ (1) x-y>0.

This implies that x>y. But it doesn't say anything about the sign of x and y. INSUFFICIENT.

(2) xy>0.

This implies that x and y has the same sign, therefore $$\frac{x}{y}>0$$ SUFFICIENT.

The correct answer should be B.

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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.

The question can be modified as follows:
x/y^3>0 => xy>0.
This can be seen by multiplying both sides by y^4.
It is same as condition 2).

Condition 1)
If x = 2 and y = 1, xy = 2 > 0, and the answer is ‘yes’.
If x = 2 and y = -1, xy = -2 < 0, and the answer is ‘no’.
Since we don’t have a unique answer, condition 1) is not sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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