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Math Revolution GMAT Instructor V
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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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) $$x^2<1$$

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Intern  B
Joined: 28 Dec 2010
Posts: 49
Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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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.
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Math Revolution GMAT Instructor V
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]

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=>

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
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Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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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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GMAT Tutor B
Joined: 07 Nov 2016
Posts: 56
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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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
_________________ 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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