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Is x > 0? 1) x^3+x^2+x<0 2) x^2<1

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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06 Nov 2017, 21:51
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:31) correct 24% (01:54) wrong based on 103 sessions

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[GMAT math practice question]

Is $$x > 0$$?

1) $$x^3+x^2+x<0$$
2) $$x^2<1$$

_________________
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" Intern Joined: 28 Dec 2010 Posts: 49 Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1 [#permalink] Show Tags 06 Nov 2017, 21:56 1. $$x^3 + x^2 + x > 0$$ $$x ( x^2 + x + 1) > 0$$ Here $$x^2 + x + 1 is always > 0$$ So x<0 Sufficient. 2. $$x^2<1$$ $$(x+1)(x-1) < 0$$ x>-1 ; x < 1 Insufficient. A. _________________ _________________________________________ Please Kudos, if you found this post helpful. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1 [#permalink] Show Tags 09 Nov 2017, 00:42 => 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. Since we have 1 variable and 0 equation, D is most likely to be the answer. Conditions 1) x^3+x^2+x<0 x(x^2+x+1)<0 implies x < 0, since x^2+x+1 > 0. The answer is no. Since “no” is also an answer according to CMT (Common Mistake Time) 1, this is sufficient. Condition 2) x^2<1 We have x2-1 < 0 and (x+1)(x-1) < 0. Thus, you get -1 < x < 1 according to the “between” rule in inequalities. This is not sufficient. Therefore, A is the answer. 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. 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. Ans: A _________________ 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: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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16 Feb 2019, 21:09
MathRevolution wrote:
[GMAT math practice question]

Is $$x > 0$$?

1) $$x^3+x^2+x<0$$
2) $$x^2<1$$

for 1, to be true, x has to be < 0

x^3 = -ive
x^2 = +ive
x = - ive

question becomes a No

Now from 2) we get -1<x<1

Which gives us a Yes or a No

A
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Joined: 07 Nov 2016
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GMAT 1: 760 Q51 V42
Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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17 Feb 2019, 00:05
MathRevolution wrote:
[GMAT math practice question]

Is $$x > 0$$?

1) $$x^3+x^2+x<0$$
2) $$x^2<1$$

St 1 : $$x^3 + x^2 + x < 0$$

$$x( x^2 +1) + x^2 < 0$$

x ( Positive Qty) + Positive Qty < 0

This means x < 0

Definite NO

Sufficient

St 2 : $$x^2 < 1$$

This means : -1 < x < 1

Not Sufficient

Choice A
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Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1   [#permalink] 17 Feb 2019, 00:05
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