Is x 0 ? (1) x^3

Question

Is x > 0 ?

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

SonalSinha803 · Answer

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 · Answer

Solution

To find:

• Whether x > 0 or not
Analysing Statement 1

• As per the information given in statement 1, \(x^3 < x\)

• 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

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

KSBGC · Answer

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.

PedroBodnar · Answer

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?

Mo2men · Answer

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.

chetan2u · Answer

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

PedroBodnar · Answer

Awesome. One more concept learned.

sukoon9334 · Answer

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

shivanks · Answer

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

chetan2u · Answer

Statement 2 says x is even, and  even  means it is an integer divisible by 2.

bumpbot · Answer

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

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