GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jan 2019, 16:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# Is x^2 > 1/x?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Jan 2015
Posts: 34

### Show Tags

29 Apr 2017, 00:36
2
5
00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:03) correct 43% (02:00) wrong based on 182 sessions

### HideShow timer Statistics

Is $$x^2 > \frac{1}{x}$$?

(1) $$x^2> x$$

(2) $$1>\frac{1}{x}$$
Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 533
Location: India
GMAT 1: 780 Q51 V46
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

29 Apr 2017, 02:22
1
Top Contributor

This is a typical inequality DS question in GMAT.

It’s a YES-NO DS question.

Before moving into the statements, start understanding for what values of x, x^2 < 1/x?

Question: x^2 < 1/x?

Let’s first try with positive integers, For x = 2, 3, 4… x^2 > 1/x, here the answer to the question is NO.

For negative values, that is, x < 0, x^2 > 1/x, here the answer to the question is NO.

For “x” a proper(positive) fraction, x = ½, ¼... x^2 < 1/x, here the answer to the question is YES.

Sometimes knowing the YES and NO answer to the question helps to solve the question better.

So, NET-NET, if 0<x<1 then the answer to the question is YES.

Or else Answer to the question is NO.

Let’s move onto statements now,

Statement I is sufficient:

x^2 > x

Except for the values between, 0<x<1, x^2 > x

So, answer to the question is always NO here.

Hence sufficient.

To understand the expression, x^2 > x

We can find the roots and draw the number line.

x^2 > x

x^2-x > 0

x(x-1) > 0

So, roots (critical points) are zero and 1.

See the below number line, to understand how it works.

Just choose values from the given (in the pic below) three ranges and check which satisfy the expression x^2 > x.

Statement II is sufficient:

1 > 1/x

That is “x” has to be negative or x has to greater than 1.

You can do some plugging in here to check it.

For x is negative, 1(positive) > negative.

For x is greater than 1, 1 > 1/x. For x = 2, 3, 4… 1 > 1/x,

So, answer to the question is always NO here.

Hence sufficient.

So, the answer has to be D (Each alone sufficient).

Hope this helps.
Attachments

number line.png [ 2.47 KiB | Viewed 1802 times ]

_________________

Register for the Free GMAT Video Training Course : https://crackverbal.com/MBA-Through-GMAT-2019-Registration

Manager
Joined: 29 May 2016
Posts: 101
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

30 Apr 2017, 09:59
by solving the equation we will get
is x^3 -1 /x >0

A) will give x >1 and x<0 in both the cases answer will be YES
B clearly sufficient
D is the answr
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 872
Location: India
GMAT 1: 710 Q49 V36
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

30 Apr 2017, 12:41
Is $$x^2 > \frac{1}{x}$$?

(1) $$x^2> x$$

(2) $$1>\frac{1}{x}$$

A says

X^2 > x

so x>1 and -1<x

for any value of x in the above range , yes would be the answer

hence A is sufficient

B says

1> 1/x

so x>1 and -1<x

for any value of x in the above range , yes would be the answer

hence B is also sufficient

hence the answer would be D
Intern
Joined: 24 Feb 2017
Posts: 35
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

17 Aug 2017, 20:35
I feel like this is easiest to solve if we visualize the problem on a number line.

Question stem asks (Y/N) if x belongs to the below Y region.

|-------------(-1)------(0)------(1)-------------|
|-------Y------|---Y---|---N---|--------Y-------|

Both from statement 1 & 2, we'll get the same YYNY on number line.

(D)
CEO
Joined: 11 Sep 2015
Posts: 3325
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

29 Mar 2018, 15:28
Top Contributor
Is $$x^2 > \frac{1}{x}$$?

(1) $$x^2> x$$

(2) $$1>\frac{1}{x}$$

Target question: Is x² > 1/x ?

Statement 1: x² > x
First off, this inequality tells us that x ≠ 0
Second, we can conclude that x² is POSITIVE.
So, we can safely divide both sides of the inequality by x² to get: 1 > 1/x
If 1 > 1/x, then there are two possible cases:
Case a: x > 1. If x is a positive number greater than 1, then 1/x will definitely be less than 1.
Case b: x is negative. If x is negative, then 1/x will definitely be less than 1.

IMPORTANT: So how do these two cases affect the answer to the target question? Let's find out.
Case a: If x > 1, then x² is greater than 1, AND 1/x is less than 1. This means x² > 1/x
Case b: If x is negative, then x² is positive, AND 1/x is negative. This means x² > 1/x
Perfect - in both cases, we get the SAME answer to the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 > 1/x
Notice that this inequality is the SAME as the inequality derived from statement 1 (we got 1 > 1/x)
Since we already saw that statement 1 is sufficient, it must be the case that statement 2 is also SUFFICIENT

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Intern
Joined: 17 Feb 2018
Posts: 10
Location: New Zealand
Concentration: Strategy, Technology
WE: Consulting (Computer Software)
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

29 Mar 2018, 22:40
CrackVerbalGMAT wrote:

This is a typical inequality DS question in GMAT.

It’s a YES-NO DS question.

Before moving into the statements, start understanding for what values of x, x^2 < 1/x?

Question: x^2 < 1/x?

Let’s first try with positive integers, For x = 2, 3, 4… x^2 > 1/x, here the answer to the question is NO.

For negative values, that is, x < 0, x^2 > 1/x, here the answer to the question is NO.

For “x” a proper(positive) fraction, x = ½, ¼... x^2 < 1/x, here the answer to the question is YES.

Sometimes knowing the YES and NO answer to the question helps to solve the question better.

So, NET-NET, if 0<x<1 then the answer to the question is YES.

Or else Answer to the question is NO.

Let’s move onto statements now,

Statement I is sufficient:

x^2 > x

Except for the values between, 0<x<1, x^2 > x

So, answer to the question is always NO here.

Hence sufficient.

To understand the expression, x^2 > x

We can find the roots and draw the number line.

x^2 > x

x^2-x > 0

x(x-1) > 0

So, roots (critical points) are zero and 1.

See the below number line, to understand how it works.

Just choose values from the given (in the pic below) three ranges and check which satisfy the expression x^2 > x.

Statement II is sufficient:

1 > 1/x

That is “x” has to be negative or x has to greater than 1.

You can do some plugging in here to check it.

For x is negative, 1(positive) > negative.

For x is greater than 1, 1 > 1/x. For x = 2, 3, 4… 1 > 1/x,

So, answer to the question is always NO here.

Hence sufficient.

So, the answer has to be D (Each alone sufficient).

Hope this helps.

Why have you not considered value of X in the range 0>x>-1??
Even though the answer does not change, the explanation will be different.
Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

29 Mar 2018, 23:11
Its a direct question.
First we will rephrase the question.
Since x^2 is greater than one we can cross divide it without changing sign now question become
1>1/x^3

option1-->(x^2)>x
cross divide with x^2
it becomes 1>(1/X) ..Since it is true then 1>(1/x^3)
option 2 is same as option 1
1>(1/X)

So D. No need to insert all the values and check
Intern
Joined: 20 Oct 2017
Posts: 26
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

02 May 2018, 10:50
CrackVerbalGMAT wrote:

This is a typical inequality DS question in GMAT.

It’s a YES-NO DS question.

Before moving into the statements, start understanding for what values of x, x^2 < 1/x?

Question: x^2 < 1/x?

Let’s first try with positive integers, For x = 2, 3, 4… x^2 > 1/x, here the answer to the question is NO.

For negative values, that is, x < 0, x^2 > 1/x, here the answer to the question is NO.

For “x” a proper(positive) fraction, x = ½, ¼... x^2 < 1/x, here the answer to the question is YES.

Sometimes knowing the YES and NO answer to the question helps to solve the question better.

So, NET-NET, if 0<x<1 then the answer to the question is YES.

Or else Answer to the question is NO.

Let’s move onto statements now,

Statement I is sufficient:

x^2 > x

Except for the values between, 0<x<1, x^2 > x

So, answer to the question is always NO here.

Hence sufficient.

To understand the expression, x^2 > x

We can find the roots and draw the number line.

x^2 > x

x^2-x > 0

x(x-1) > 0

So, roots (critical points) are zero and 1.

See the below number line, to understand how it works.

Just choose values from the given (in the pic below) three ranges and check which satisfy the expression x^2 > x.

Statement II is sufficient:

1 > 1/x

That is “x” has to be negative or x has to greater than 1.

You can do some plugging in here to check it.

For x is negative, 1(positive) > negative.

For x is greater than 1, 1 > 1/x. For x = 2, 3, 4… 1 > 1/x,

So, answer to the question is always NO here.

Hence sufficient.

So, the answer has to be D (Each alone sufficient).

Hope this helps.

Isn't the question x^2 > 1/x?
Intern
Joined: 01 Apr 2012
Posts: 16
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

04 May 2018, 01:50
Is $$x^2 > \frac{1}{x}$$?

(1) $$x^2> x$$

(2) $$1>\frac{1}{x}$$

Hi could someone let me know if my solution is correct.

The question asks is x^2 > 1/x
I reduced the question to is x^3 > 1 by multiplying both sides by x

Option 1: x^2 > x ,
Divide both sides by x it reduces to x>1 , If x>1 then it implies x^3 > 1
Hence Sufficient

Option 2: 1>1/x ,

Multiplying both sides by x it reduces to x>1, If x>1 then it implies x^3 > 1
Hence sufficient

Bunuel or anyone guide me by letting me know if my approach is correct.
Intern
Joined: 04 May 2018
Posts: 1
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

04 May 2018, 02:18
This is true only if variable value of X is positive.

Sent from my CPH1609 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: Is x^2 > 1/x?  [#permalink]

### Show Tags

04 May 2018, 02:43
1
vikramnugge wrote:
Is $$x^2 > \frac{1}{x}$$?

(1) $$x^2> x$$

(2) $$1>\frac{1}{x}$$

Hi could someone let me know if my solution is correct.

The question asks is x^2 > 1/x
I reduced the question to is x^3 > 1 by multiplying both sides by x

Option 1: x^2 > x ,
Divide both sides by x it reduces to x>1 , If x>1 then it implies x^3 > 1
Hence Sufficient

Option 2: 1>1/x ,

Multiplying both sides by x it reduces to x>1, If x>1 then it implies x^3 > 1
Hence sufficient

Bunuel or anyone guide me by letting me know if my approach is correct.

$$x^2 > \frac{1}{x}$$ is not the same as $$x^3>1$$. You cannot multiply the inequality by x because you don't know its sign. If x is positive, then yes, $$x^2 > \frac{1}{x}$$ is equivalent to x^3 > 1 but if x is negative, then when you multiply by negative value you should flip the sign, so in this case you'll get: x^3 < 1.

The same for (1) and (2): never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

_________________
Re: Is x^2 > 1/x? &nbs [#permalink] 04 May 2018, 02:43
Display posts from previous: Sort by