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Is x > 0 ? (1) x^3 < x (2) x is even.

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Bunuel
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Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   05 Jun 2018, 00:26
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Is x > 0 ?

(1) x^3 < x
(2) x is even.
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C
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SonalSinha803
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   05 Jun 2018, 01:24
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According to statement 1, x can be negative or fraction less than 1 and greater than zero.
Thus, insufficient.

According to statement 2, x can be either positive or negative even integer.
Insufficient.

Combining the two statements, x is even integer only and negative definitely. Thus, we know, x<0. Hence, sufficient.

Thus, C.

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EgmatQuantExpert
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   05 Jun 2018, 02:17
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Solution



To find:
    • Whether x > 0 or not

Analysing Statement 1
    • As per the information given in statement 1, \(x^3 < x\)
      Simplifying, \(x^3 – x < 0\)
      Or, \(x (x^2 – 1) < 0\)
      Or, \(x (x – 1) (x + 1) < 0\)

    • This is true when 0 < x < 1 or x < -1

Since x can be both positive or negative, we cannot say whether x > 0 or not

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, x is even
    • The value of x, being even, can be both positive and negative

Hence, statement 2 is not sufficient to answer

Combining Both Statements
If we combine the information present in both the statements, we can say
    • The value of x lies in the range x < -1 as there are no even integers possible in 0 < x < 1.

Therefore, we can say x is not greater than 0

Hence, the correct answer is option C.

Answer: C
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   05 Jun 2018, 02:59
Bunuel wrote:
Is x > 0 ?

(1) x^3 < x
(2) x is even.


we don't know whether x is integer or fraction or negative or positive.

statement 1 :\(x^3\)<x. this statement is true when x is fraction or negative. So, we can determine whether x>0 or not.
statement 2 : x is even. but here x can also be negative or positive. Not sufficient.

combining (1+2): analyzing both statements we understand that x is negative and even integer.

Thus, x is not positive for sure. So, the correct answer is C.
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PedroBodnar
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   08 Jun 2018, 17:46
Can a fraction be considered an even number?

From my perspective, it was not mentioned that x was an integer. Then, 0.2 (or 1/5), which I (with no grounds) consider an even number, would lead the answer to an E.

Can someone please clarify this?
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   08 Jun 2018, 18:43
PedroBodnar wrote:
Can a fraction be considered an even number?

From my perspective, it was not mentioned that x was an integer. Then, 0.2 (or 1/5), which I (with no grounds) consider an even number, would lead the answer to an E.

Can someone please clarify this?


fraction is a number either positive or negative but it is NOT an integer. This is known fact. It is not needed to be mentioned.
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chetan2u
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   08 Jun 2018, 20:50
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PedroBodnar wrote:
Can a fraction be considered an even number?

From my perspective, it was not mentioned that x was an integer. Then, 0.2 (or 1/5), which I (with no grounds) consider an even number, would lead the answer to an E.

Can someone please clarify this?


Only integers can be odd or even.
So even or odd means it is an integer
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PedroBodnar
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   09 Jun 2018, 05:18
chetan2u wrote:
PedroBodnar wrote:
Can a fraction be considered an even number?

From my perspective, it was not mentioned that x was an integer. Then, 0.2 (or 1/5), which I (with no grounds) consider an even number, would lead the answer to an E.

Can someone please clarify this?


Only integers can be odd or even.
So even or odd means it is an integer


Awesome. One more concept learned.

:)
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   30 Nov 2019, 01:19
EgmatQuantExpert wrote:

Solution



To find:
    • Whether x > 0 or not

Analysing Statement 1
    • As per the information given in statement 1, \(x^3 < x\)
      Simplifying, \(x^3 – x < 0\)
      Or, \(x (x^2 – 1) < 0\)
      Or, \(x (x – 1) (x + 1) < 0\)

    • This is true when 0 < x < 1 or x < -1

Since x can be both positive or negative, we cannot say whether x > 0 or not

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
    • As per the information given in statement 2, x is even
    • The value of x, being even, can be both positive and negative

Hence, statement 2 is not sufficient to answer

Combining Both Statements
If we combine the information present in both the statements, we can say
    • The value of x lies in the range x < -1 as there are no even integers possible in 0 < x < 1.

Therefore, we can say x is not greater than 0

Hence, the correct answer is option C.

Answer: C


In the equation (x-1)(x)(x+1)<O, (x-1) < 0 => x<1; (x+1)<0 => x<-1, then shouldn't x<0 be also considered?
You've concluded that 0<x<1. Couldn't understand that part.

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shivanks
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   13 Jan 2024, 11:55
KSBGC wrote:
Bunuel wrote:
Is x > 0 ?

(1) x^3 < x
(2) x is even.


we don't know whether x is integer or fraction or negative or positive.

statement 1 :\(x^3\)<x. this statement is true when x is fraction or negative. So, we can determine whether x>0 or not.
statement 2 : x is even. but here x can also be negative or positive. Not sufficient.

combining (1+2): analyzing both statements we understand that x is negative and even integer.

Thus, x is not positive for sure. So, the correct answer is C.

I'm confuse how can u assume after combining the statement that x is integer???
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chetan2u
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink] New post   13 Jan 2024, 12:00
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shivanks wrote:
KSBGC wrote:
Bunuel wrote:
Is x > 0 ?

(1) x^3 < x
(2) x is even.


we don't know whether x is integer or fraction or negative or positive.

statement 1 :\(x^3\)<x. this statement is true when x is fraction or negative. So, we can determine whether x>0 or not.
statement 2 : x is even. but here x can also be negative or positive. Not sufficient.

combining (1+2): analyzing both statements we understand that x is negative and even integer.

Thus, x is not positive for sure. So, the correct answer is C.

I'm confuse how can u assume after combining the statement that x is integer???



Statement 2 says x is even, and even means it is an integer divisible by 2.
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Re: Is x > 0 ? (1) x^3 < x (2) x is even. [#permalink]
13 Jan 2024, 12:00
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