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

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
If x > 0, which of the following could be true?  [#permalink]

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03 Dec 2014, 07:18
2
12
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:57) correct 31% (00:56) wrong based on 418 sessions

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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]

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03 Dec 2014, 08:23
2
1
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]

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03 Dec 2014, 19:13
1
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

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Re: If x > 0, which of the following could be true?  [#permalink]

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03 Dec 2014, 20:22
1
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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Posts: 52902
Re: If x > 0, which of the following could be true?  [#permalink]

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04 Dec 2014, 06:13
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]

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24 Dec 2014, 11:28
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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Joined: 18 Jan 2010
Posts: 251
Re: If x > 0, which of the following could be true?  [#permalink]

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30 May 2016, 04:04
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)

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Re: If x > 0, which of the following could be true?  [#permalink]

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27 May 2017, 17:22
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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Concentration: Finance, Statistics
Re: If x > 0, which of the following could be true?  [#permalink]

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30 Aug 2018, 12:28
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
Re: If x > 0, which of the following could be true?   [#permalink] 30 Aug 2018, 12:28
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