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

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Bunuel
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If x > 0, which of the following could be true? [#permalink] New post   03 Dec 2014, 08:18
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A
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D
E

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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
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D
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Re: If x > 0, which of the following could be true? [#permalink] New post   03 Dec 2014, 09:23
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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)
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Re: If x > 0, which of the following could be true? [#permalink] New post   03 Dec 2014, 20:13
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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
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Re: If x > 0, which of the following could be true? [#permalink] New post   03 Dec 2014, 21:22
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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
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Re: If x > 0, which of the following could be true? [#permalink] New post   24 Dec 2014, 12:28
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
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Re: If x > 0, which of the following could be true? [#permalink] New post   30 May 2016, 05:04
Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



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

Kudos for a correct solution.


Source: Chili Hot GMAT



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
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Re: If x > 0, which of the following could be true? [#permalink] New post   27 May 2017, 18:22
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.
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Re: If x > 0, which of the following could be true? [#permalink] New post   30 Aug 2018, 13:28
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
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Re: If x > 0, which of the following could be true? [#permalink] New post   25 Sep 2019, 15:54
for statement 1, why we do not consider fractional number because it says x>0 only for example x= 1/2 ,1/4
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Re: If x > 0, which of the following could be true? [#permalink] New post   25 Sep 2019, 18:40
Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



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

Kudos for a correct solution.

Source: Chili Hot GMAT


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
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Re: If x > 0, which of the following could be true? [#permalink] New post   23 Mar 2020, 20:13
Concept tested: anomaly of [-1,1] 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 :lol:


Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



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

Kudos for a correct solution.

Source: Chili Hot GMAT
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Re: If x > 0, which of the following could be true? [#permalink] New post   08 Sep 2023, 11:03
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
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Re: If x > 0, which of the following could be true? [#permalink] New post   09 Sep 2023, 04:37
Why did we not consider fractions and decimals? Like in case of 0.5, only 3 is true
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Re: If x > 0, which of the following could be true? [#permalink] New post   09 Sep 2023, 04:45
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thelady02 wrote:
Why did we not consider fractions and decimals? Like in case of 0.5, only 3 is true


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.
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Re: If x > 0, which of the following could be true? [#permalink] New post   24 Oct 2023, 21:51
Bunuel wrote:
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



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
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Re: If x > 0, which of the following could be true? [#permalink]
24 Oct 2023, 21:51
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