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

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Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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New post 06 Nov 2017, 21:51
00:00
A
B
C
D
E

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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Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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New post 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.
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Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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New post 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
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Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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New post 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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Re: Is x > 0? 1) x^3+x^2+x<0 2) x^2<1  [#permalink]

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New post 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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