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

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

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New post 03 Dec 2014, 08:18
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A
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D
E

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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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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]

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New post 03 Dec 2014, 20:13
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

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

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New post 03 Dec 2014, 21:22
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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Re: If x > 0, which of the following could be true?  [#permalink]

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New post 04 Dec 2014, 07:13
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


The correct answer is D.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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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]

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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]

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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]

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Re: If x > 0, which of the following could be true? &nbs [#permalink] 11 Jul 2018, 00:47
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