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If uv<0, is u^99v^100<0?

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If uv<0, is u^99v^100<0?

by Max@Math Revolution » Mon Feb 19, 2018 11:28 pm
[GMAT math practice question]

$$If\ uv<0,\ is\ u^{99}v^{100}<0?$$

$$\left(1\right)\ u<0$$
$$\left(2\right)\ v>0$$
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Feb 22, 2018 1:02 am
=>

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.

In an inequality that has the right-hand side equal to 0, even exponents can be ignored.
Asking if u^99v^100<0 is equivalent to asking if u < 0: simply divide both sides by u^98v^100 (> 0). We only need to consider the variables with odd exponents. Since the exponent of u is 99, which is an odd number, we must have u < 0. In addition, since uv < 0 by the original condition, u < 0 implies that v > 0. Thus, condition 1) is equivalent to condition 2), and D is most likely to be the answer by Tip 1).

Therefore, the answer is D.

Answer: D

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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