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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82

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20 Feb 2018, 00:36
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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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MathRevolution: 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 $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 08 Sep 2008 Posts: 134 Location: India Concentration: Operations, General Management Schools: ISB '20 GPA: 3.8 WE: Operations (Transportation) Re: If uv<0, is u^99v^100<0? [#permalink] ### Show Tags 20 Feb 2018, 01:31 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) Sent from my ASUS_Z010D using GMAT Club Forum mobile app _________________ Regards; Vishal +==========+ Kudos if it deserve....one... Manager Joined: 26 Sep 2017 Posts: 95 Re: If uv<0, is u^99v^100<0? [#permalink] ### Show Tags 21 Feb 2018, 10:40 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 Retired Moderator Joined: 22 Aug 2013 Posts: 1428 Location: India Re: If uv<0, is u^99v^100<0? [#permalink] ### Show Tags 21 Feb 2018, 10:56 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 Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If uv<0, is u^99v^100<0? [#permalink] ### Show Tags 22 Feb 2018, 02:08 => 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. 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. _________________ MathRevolution: 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$79 for 1 month Online Course"
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Re: If uv<0, is u^99v^100<0?   [#permalink] 22 Feb 2018, 02:08
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