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

 It is currently 18 Feb 2019, 07:11

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard (\$149)", get free Daily quiz (2 mon). Coupon code : SPECIAL

# How many of the following inequalities are possible for at least one

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 03 May 2016
Posts: 11
Location: United States (FL)
Concentration: Technology, Strategy
GMAT 1: 690 Q49 V34
GPA: 3
WE: Information Technology (Computer Software)
How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

Updated on: 03 Jul 2017, 02:23
7
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:49) correct 41% (01:52) wrong based on 298 sessions

### HideShow timer Statistics

How many of the following inequalities are possible for at least one value of x?

I. $$x^2 > x > x^3$$

II. $$x^2 > x^3 > x$$

III. $$x^3 > x > x^2$$

A. I only
B. II only
C. I and II only
D. I, II, and III only
E. none

Originally posted by tommannanchery on 31 Jul 2016, 11:21.
Last edited by Bunuel on 03 Jul 2017, 02:23, edited 2 times in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

31 Jul 2016, 21:37
3
3
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

The question is based on your understanding of how x, x^2 and x^3 behave in different regions of the number line.

x^2 > x for all negative x and when x > 1
x^3 > x for x > 1 and -1 < x < 0.

(i) $$x^2$$ > X > $$x^3$$
True for all negative x.

(ii) $$x^2$$ > $$x^3$$ > X
True for -1 < x< 0

(iii) $$x^3$$ > X > $$x^2$$
x is greater than x^2 between 0 and 1 only. But in that region x^3 is not greater than x. So this will not hold.

_________________

Karishma
Veritas Prep GMAT Instructor

##### General Discussion
VP
Joined: 05 Mar 2015
Posts: 1001
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

Updated on: 01 Aug 2016, 06:31
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

(1) Let X=-2 then we get a yes answer
(2) Let X=-0.5 then we get a yes
(3) none of X satisfies

Ans C

Originally posted by rohit8865 on 31 Jul 2016, 18:15.
Last edited by rohit8865 on 01 Aug 2016, 06:31, edited 2 times in total.
Intern
Joined: 21 Sep 2015
Posts: 5
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

01 Aug 2016, 00:26
Answer should be C. iii is incorrect because when x > x2, which is when 0
Posted from my mobile device
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3631
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

01 Aug 2016, 07:30
1
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

For (i) - Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27

For (ii)- Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8.

For (iii) - Consider x= 2 => We can have X = 5 which is between 8 and 4.

Hence, we can have each of the above statements valid for different vales of x and X.

NOTE : I have solved the above question based on the assumption that x and X are two different variables.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

VP
Joined: 05 Mar 2015
Posts: 1001
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

01 Aug 2016, 08:29
1
abhimahna wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

For (i) - Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27

For (ii)- Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8.

For (iii) - Consider x= 2 => We can have X = 5 which is between 8 and 4.

Hence, we can have each of the above statements valid for different vales of x and X.

NOTE : I have solved the above question based on the assumption that x and X are two different variables.

if the highlighted part is correct then there is no need of any option there always exist a number in between

Karishma

Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3631
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

01 Aug 2016, 08:45
rohit8865 wrote:
abhimahna wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

For (i) - Consider x=1/3. => We can have X= 2/27 which is between 1/9 and 1/27

For (ii)- Consider x= 1/2= > We can have X=0 which is less than 1/4 and 1/8.

For (iii) - Consider x= 2 => We can have X = 5 which is between 8 and 4.

Hence, we can have each of the above statements valid for different vales of x and X.

NOTE : I have solved the above question based on the assumption that x and X are two different variables.

if the highlighted part is correct then there is no need of any option there always exist a number in between

Karishma

Correct bro. I agree to what you said.

_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

26 Mar 2017, 21:11
VeritasPrepKarishma wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

The question is based on your understanding of how x, x^2 and x^3 behave in different regions of the number line.

x^2 > x for all negative x and when x > 1
x^3 > x for x > 1 and -1 < x < 0.

(i) $$x^2$$ > X > $$x^3$$
True for all negative x.

(ii) $$x^2$$ > $$x^3$$ > X
True for -1 < x< 0

(iii) $$x^3$$ > X > $$x^2$$
x is greater than x^2 between 0 and 1 only. But in that region x^3 is not greater than x. So this will not hold.

Responding to a pm:
Quote:
I have a doubt for the second one?

-0.5 (-1/2) lies in the range -1<x<0

so if we consider x=-1/2; then x2 = -1/4 and x3 = -1/8

in this case x3>x2>x -_. so second case does not hold

Note that square of a real number is never negative.

If

$$x = -1/2,$$

$$x^2 = (-1/2)^2 = (-1/2)*(-1/2) = 1/4$$

$$x^3 = (-1/2)*(-1/2)*(-1/2) = -1/8$$

So
$$x^2 > x^3 > x$$
_________________

Karishma
Veritas Prep GMAT Instructor

Retired Moderator
Joined: 04 Aug 2016
Posts: 487
Location: India
GPA: 4
WE: Engineering (Telecommunications)
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

03 Jul 2017, 02:16
1
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

Bunuel: Can you please check this question? I did not find any values for which (iii) holds. Shouldn't OA be C?
Math Expert
Joined: 02 Sep 2009
Posts: 52935
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

03 Jul 2017, 02:24
warriorguy wrote:
tommannanchery wrote:
How many of the following equalities are possible for at least one value of X?

(i) $$x^2$$ > X > $$x^3$$
(ii) $$x^2$$ > $$x^3$$ > X
(iii) $$x^3$$ > X > $$x^2$$

A. i only
B. ii only
C. i and ii only
D. i, ii, and iii only
E. none

Bunuel: Can you please check this question? I did not find any values for which (iii) holds. Shouldn't OA be C?

Yes. The correct answer is C, not D. Edited. Thank you.
_________________
Manager
Joined: 24 Sep 2018
Posts: 139
Re: How many of the following inequalities are possible for at least one  [#permalink]

### Show Tags

02 Oct 2018, 00:44
saichandm wrote:
Answer should be C. iii is incorrect because when x > x2, which is when 0<x<1), x3 is less than x2!!

Posted from my mobile device

For a problem that hinges on a conceptual understanding of properties of numbers with exponents, plugging in is a natural first approach. So try values in meaningfully different ranges. Say x is 2: that makes
$$x^2$$=4
and $$x^3$$=8
$$So, x^3 > x^2 > x$$
which doesn't work for any of the inequalities.
Now say x is -2: that makes $$x^2$$
$$x^3$$=-8

$$So, x^2 > x > x^3$$

Having tried both negative and positive integers, consider what other ranges are left: fractions between 0 and 1 and fractions between 0 and 1. Inequality (ii) will be true for any fraction between 0 and -1, so it's possible, but inequality (iii) never works: the only numbers for which x > $$x^2$$ are fractions between 0 and 1, but for all such numbers $$x^2$$ is also greater than $$x^3$$

_________________

Please award kudos, If this post helped you in someway.

Re: How many of the following inequalities are possible for at least one   [#permalink] 02 Oct 2018, 00:44
Display posts from previous: Sort by