Is x 0 (1) x^2 x (2) x^3 x

Question

Is x > 0

(1) x^2 > x
(2) x^3 > x

Temurkhon · Answer

algebraic approach looks best St1. x^2>x x^2-x>0 x(x-1)>0, so x>0 OR x<0. INSUFF St2. x^3>x x^3-x>0 x(x^2-1)>0, so x>0 OR x<0. INSUFF St1+St2. Still have x>0 OR x<0. INSUFF E

Lucky2783 · Answer

(1) x^2 > x Or x(x-1) >0 x=4 x=-5 both satisfies the equation. Not Sufficient. (2) x^3 > x x(x^2-1)>0 X=2 X=\frac{-1}{2} Both satisfies the equation so Not Sufficient. Together: x(x-1)(x+1) + x(x-1) > 0 x(x-1) (x+2)>0 clearly -21 both satisfies this inequality . Answer E see attached image .

ravinder050484 · Answer

I can't understand why is first option insufficient.

x^2>x
x^2-x>0
x(x-1)>0
x>0 or x>1 which gives me the answer. but this is not the correct answer. can some one please explain me

abhinav008 · Answer

When u substitute x> 1 say x = 1.1 1.1 ( 1.1-1 ) is greater than 0 When substitute X between 0 and 1 you can see that 0.5 ( 0.5 -1 ) is less than 0 When substitute value x< 0 say -0.5 -0.5 ( -0.5 - 1 ) we get value > 0 So the equation satisfies all values except values between 0 and 1 So X> 0 i.e 1.1 or less than 0 i.e. -0.5 both these values when substituted in x ( x-1 ) gives answer > 0 So X can be > 1 or x can be < 0

EgmatQuantExpert · Answer

Hi ravinder050484 , For the inequality x(x-1) > 0, there are a couple of ways to find out the range of x. Method-1 You can interpret this inequality as product of two numbers being greater than 0 i.e. it tells us about the same sign of the numbers. So, either a. x & x-1 both are positive which would be true for range x > the largest zero point i.e. x > 1 or b. x & x-1 both are negative which would be true for range x < the smallest zero point i.e. x < 0. Combining these two we can say that x > 1 or x < 0. Thus statement-I is insufficient to answer the question. Method-2 You can find the range of this inequality using the Wavy line method. Refer the following diagram for the range of x . https://e-gmat.com/blogs/wp-content/uploads/2015/05/GC-Wavy-line-4-e1431060064651.jpg We can see from the wavy line diagram that the inequality is positive when x > 1 or x < 0. Thus we can't say for sure if x > 0. Hence, statement-I is insufficient to answer the question. You can read more about the Wavy Line method here Hope its clear! Regards Harsh

EMPOWERgmatRichC · Answer

Hi abhinav008,

This DS question can be solved with a combination of Number Properties and TESTing VALUES.

We're asked if X > 0. This is a YES/NO question.

Fact 1: X^2 > X

IF...
X = 2
the answer to the question is YES.

IF...
X = ANY NEGATIVE
the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: X^3 > X

IF....
X = 2
the answer to the question is YES.

IF...
X = -1/2
the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
X^2 > X
X^3 > X

From our prior work, we have VALUES that 'fit' BOTH Facts, so we know....

IF....
X = 2
the answer to the question is YES.

IF...
X = -1/2
the answer to the question is NO.
Combined, INSUFFICIENT

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

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Is x > 0 (1) x^2 > x (2) x^3 > x

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