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# Is k + 1/k < -1 ?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5855
GMAT 1: 760 Q51 V42
GPA: 3.82
Is k + 1/k < -1 ?  [#permalink]

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10 Oct 2017, 06:06
2
2
00:00

Difficulty:

65% (hard)

Question Stats:

49% (02:05) correct 51% (02:00) wrong based on 45 sessions

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Is k + 1/k < -1 ?

1) k^2 < 1
2) k^3 + k^2 + k < 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 $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 6253 Is k + 1/k < -1 ? [#permalink] ### Show Tags 10 Oct 2017, 06:43 MathRevolution wrote: Is k + 1/k < -1 ? 1) k^2 < 1 2) k^3 + k^2 + k < 0 Hi.. $$k+\frac{1}{k}<-1......(\frac{1+k+1}{k})<0.....\frac{(k^2+k+1)}{k}<0$$... So both numerator and denominator should be of opposite sign.. If $$k<0, k^2+k+1>0$$.... If $$k>0, k^2+k+1<0$$....not possible 1) $$k^2<1$$ Insufficient 2) $$k^3+k^2+k<0....... K(k^2+k+1)<0..$$ So $$k$$ and $$k^2+k+1$$ are of opposite sign. This is same as the initial equation Sufficient B Posted from my mobile device _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5855 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is k + 1/k < -1 ? [#permalink] ### Show Tags 12 Oct 2017, 01:44 Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. k + 1/k < 1 is equivalent to k3 + k < -k2 or k3 + k2 + k < 0. k(k2 + k + 1) < 0 implies k < 0, since k2 + k + 1 is always positive. Thus, the simplified question is if k < 0. Condition 1) k2< 1 It is equivalent to -1 < k < 1. Thus,this is not sufficient. Condition 2) k3 + k2 + k < 0 Thus, is equivalent to the question. This is sufficient. Therefore, the answer is B. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Then, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, 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$99 for 3 month Online Course"
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Re: Is k + 1/k < -1 ? &nbs [#permalink] 12 Oct 2017, 01:44
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