Author 
Message 
TAGS:

Hide Tags

Current Student
Joined: 03 May 2016
Posts: 11
Location: United States (FL)
Concentration: Technology, Strategy
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, 03:23
Question Stats:
57% (01:00) correct 43% (00:59) wrong based on 290 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by tommannanchery on 31 Jul 2016, 12:21.
Last edited by Bunuel on 03 Jul 2017, 03:23, edited 2 times in total.
Renamed the topic and edited the question.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8397
Location: Pune, India

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
31 Jul 2016, 22:37
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) \(x^2\) > \(x^3\) > XTrue 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. Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Director
Joined: 05 Mar 2015
Posts: 995

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
Updated on: 01 Aug 2016, 07:31
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, 19:15.
Last edited by rohit8865 on 01 Aug 2016, 07:31, 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, 01:26
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: 3622

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
01 Aug 2016, 08:30
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 Answer is D. 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 Blog: Subscribe to Question of the Day Blog
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.



Director
Joined: 05 Mar 2015
Posts: 995

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
01 Aug 2016, 09:29
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 Answer is D. 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 Please give your 2 cents also because source mentioned is veritas...



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3622

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
01 Aug 2016, 09:45
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 Answer is D. 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 Please give your 2 cents also because source mentioned is veritas... Correct bro. I agree to what you said. Can anyone please help here?
_________________
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 Blog: Subscribe to Question of the Day Blog
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: 8397
Location: Pune, India

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
26 Mar 2017, 22:11
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) \(x^2\) > \(x^3\) > XTrue 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. Answer (C) 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Retired Moderator
Joined: 04 Aug 2016
Posts: 517
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
03 Jul 2017, 03:16
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: 50003

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
03 Jul 2017, 03:24



Manager
Joined: 24 Sep 2018
Posts: 115

Re: How many of the following inequalities are possible for at least one
[#permalink]
Show Tags
02 Oct 2018, 01:44
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 \(x^3\) Answer C
_________________
Please award kudos, If this post helped you in someway.




Re: How many of the following inequalities are possible for at least one &nbs
[#permalink]
02 Oct 2018, 01:44






