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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
If uv<0, is u^99v^100<0?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 67% (00:59) correct 33% (01:02) wrong based on 75 sessions

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[GMAT math practice question]

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

$$1) u<0$$
$$2) v>0$$

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Manager  S
Joined: 08 Sep 2008
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Location: India
Concentration: Operations, General Management
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Re: If uv<0, is u^99v^100<0?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

$$1) u<0$$
$$2) v>0$$

UV<0 So u and v has opposite sign.

Each statement gives the sign of either u or v.
So each statements is sufficient to answer the question.

Ans: D (imo)

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Manager  B
Joined: 26 Sep 2017
Posts: 95
Re: If uv<0, is u^99v^100<0?  [#permalink]

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Ans is A..

Given uv <0..
Means either u or v must be -ve...

In qus it is given v^100 which is alwys +ve..
So evrythng depends upon u...
It means only A satisfies..

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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: If uv<0, is u^99v^100<0?  [#permalink]

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viv007 wrote:
Ans is A..

Given uv <0..
Means either u or v must be -ve...

In qus it is given v^100 which is alwys +ve..
So evrythng depends upon u...
It means only A satisfies..

Sent from my BND-AL10 using GMAT Club Forum mobile app

Hi

You are correct that either u or v must be negative and you are also correct that since 'v' is raised to an even power, it will always be positive, so it depends on 'u'.

But when its given in statement 2 that v is positive, doesn't it automatically mean that 'u' is negative, making it the same case as statement 1. So since u is negative, product of u^99*v^100 will be negative. Thus answer should be D.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If uv<0, is u^99v^100<0?  [#permalink]

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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, and then recheck the question.

In an inequality that has the right-hand side equal to 0, even exponents can be ignored.
Asking if $$u^{99}v^{100}<0$$ is equivalent to asking if $$u < 0$$: simply divide both sides by $$u^{98}v^{100} (> 0)$$. 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.

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.
_________________ Re: If uv<0, is u^99v^100<0?   [#permalink] 22 Feb 2018, 02:08
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