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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 50% (01:07) correct 50% (01:14) wrong based on 112 sessions

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Is x > 0 ?

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

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Senior Manager  G
Joined: 14 Feb 2018
Posts: 386
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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1
1
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.

Posted from my mobile device
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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1
2

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.

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Joined: 31 Oct 2013
Posts: 1491
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.
Intern  B
Joined: 11 Feb 2016
Posts: 13
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.

SVP  V
Joined: 26 Mar 2013
Posts: 2343
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.

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.
Math Expert V
Joined: 02 Aug 2009
Posts: 8288
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.

Only integers can be odd or even.
So even or odd means it is an integer
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Intern  B
Joined: 11 Feb 2016
Posts: 13
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.

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

Awesome. One more concept learned. Intern  B
Joined: 22 Oct 2019
Posts: 13
Location: India
Schools: HEC Montreal '21
Re: Is x > 0 ? (1) x^3 < x (2) x is even.  [#permalink]

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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.

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.

Posted from my mobile device Re: Is x > 0 ? (1) x^3 < x (2) x is even.   [#permalink] 30 Nov 2019, 01:19
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