If x 0, which of the following could be true?

Question

If x > 0, which of the following could be true?

I. x^3 > x^2
II. x^2 = x
III. x^2 > x^3

A) I only
B) I & II
C) II & III
D) All of the above
E) None of the above

Source: Chili Hot GMAT

omegacube · Accepted Answer

Aha! Could, must are deadly words in DS...

1. x^3 > x^2 Well this is true for all x > +1 (but not for values 0 < x < 1)
2. x^2 = x This is true for only one positive number, 1
3. x^2 > x^3 Again this is true only for values of x such that 0 < x < 1

So the answer is D, since there exists at least one value of x which satisfies the equation/ in equation(s)

PareshGmat · Answer

Answer = D) All of the above

I.  x^3 > x^2

For x = 2,

2^3 > 2^2

II.  x^2 = x

For x = 1,

1^2 = 1

III.  x^2 > x^3

For  x = \frac{1}{2},

(\frac{1}{2})^2 > (\frac{1}{2})^3

All conditions could satisfy

Answer = D

JJo · Answer

Since, it is asked 'could be true' we can use any 1 case which satisfies the equation and consider it as true.
x>0

I. x^3 > x^2 --> 10^3>10^2 -- true
II. x^2 = x --> 1^2 = 1 -- true
III. x^2 > x^3 --> (1/2)^2>(1/2)^3 -- true

Ans. D) All of the above

veergmat · Answer

For x>0;

I. x^3 > x^2 .............. when x>1
II. x^2 = x ..................when x=1
III. x^2 > x^3.............. when x<1

adiagr · Answer

I. x^3 > x^2
 This statement is true for any x > 1.

So C and E cannot be correct option.

II. x^2 = x

This statement is true for x = 1.

So A cannot be correct option.

III. x^2 > x^3

This is true for any x > 0 but < 1 say x = (1/2)

So Correct Answer is D

Heseraj · Answer

The world could be defines the entire logic of this question: Cases like this, one needs only one case to hold the question

Option one for any number bigger than one is true. 
Option two for number one, Variable X, is true and 
Option three for any number between 0 and 1 is true.

Should the world "could be" be "must be", instead, none would be true. Cases that ask for must be trough, on the other hand, one needs all examples to hold which makes its refuge very easy by bringing only example that doesn't hold.

manjot123 · Answer

solved by taking values 
x^3> x^2
take x = 2 
x^3>x^2
x^2= x
take x = 1
x^2> x^3
take x = 1/2

anubhav31 · Answer

for statement 1, why we do not consider fractional number because it says x>0 only for example x= 1/2 ,1/4

Kinshook · Answer

If x=2; x^3>x^2
If x=1; x^2=x
If x=.5;x^2>x^3

IMO D

Posted from my mobile device

LeoN88 · Answer

Concept tested: anomaly of bracket. Good sum! Could be true means there is a possibility that equation holds- I. x^3 > x^2, true for x=5, so could be true. II. x^2 = x true for x=1, so could be true. III. x^2 > x^3 true for x=0.5, so could be true. All I+II+III could be true. Chili Hot GMAT

Paras96 · Answer

If x > 0, which of the following could be true?

This is a could-be-true question so we can take cases where the option will hold true

I. x^3 > x^2 true for x>1 
II. x^2 = x true for x=1 
III. x^2 > x^3 true for x<1

Hence D

thelady02 · Answer

Why did we not consider fractions and decimals? Like in case of 0.5, only 3 is true

Bunuel · Answer

Note that the question asks "which of the following  could  be true?" not "which of the following  must  be true?". Since each option could be true for some values of x, the answer is D.

nivivacious · Answer

Note, we're only looking for could be true and not must be true.
If x > 0
I. x^3 > x^2 .. Yes, integer greater than 1
II. x^2 = x .. Yes, x can be equal to 1
III. x^2 > x^3 .. Yes, x can be a positive fraction

Hence
D) All of the above

If x > 0, which of the following could be true?

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GMAT Problem Solving (PS) Questions

If x > 0, which of the following could be true?

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