Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58464

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:00
Question Stats:
38% (01:34) correct 62% (01:37) wrong based on 106 sessions
HideShow timer Statistics
If x^3 < x^2, what is the value of the integer x? (1) x < 2 (2) x^3 = x
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Aug 2009
Posts: 8023

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:21
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x \(x^3 < x^2.......x^2x^3>0.....x^2(1x)>0\) therefore 1x>0 or x<1 but \(x\neq{0}\) (1) x < 2 so 2<x<2... possible values = 1,0,1 but x<1 and not equal to 1, so only value left 1 sufficient (2) x^3 = x \(x^3=x.....x^3x=0......x(x^21)=0\) so x=o or x^2=1 that is 1 and 1 but as seen above only 1 is possible out of 1,0 and 1 sufficient D
_________________



Manager
Joined: 11 May 2018
Posts: 114
Location: India

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:31
Quote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x Please correct me if I am wrong:Given x^3<x^2 x^3x^2<0 x^2(x1)<0 x<0 or x<1 Quote: STATEMENT 1:
x<2: 2<x<2 means x can be 1,0,1: If we take x<0 then we will have x=1 so suff If we take x<1 then x can be 0 or 1 so two solutions not possible Hence statement 1 is not sufficient. Quote: STATEMENT 2:
x^3=x x^3x=0 x(x^21)=0 x=0 or x=1 we have x= 1,0,1; Same as statement 1 ; so not sufficient . combining 1+2 even after clubbing both the statements we have the same result. so the answer must be E.
_________________
If you want to Thank me Give me a KUDOS "I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT" SonGoku



Manager
Joined: 11 May 2018
Posts: 114
Location: India

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:36
Thanks chetan2uI have not counted that x not equal to 0 so the answer i got was completely wrong
_________________
If you want to Thank me Give me a KUDOS "I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT" SonGoku



Math Expert
Joined: 02 Aug 2009
Posts: 8023

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:39
SonGoku wrote: Thanks chetan2uI have not counted that x not equal to 0 so the answer i got was completely wrong yes, the question is tricky in that sense, one can easily miss out on this aspect. therefore look at each question for the hidden meaning too
_________________



VP
Joined: 09 Mar 2016
Posts: 1230

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:40
chetan2u wrote: Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x \(x^3 < x^2.......x^2x^3>0.....x^2(1x)>0\) therefore 1x>0 or x<1 but \(x\neq{0}\) (1) x < 2 so 2<x<2... possible values = 1,0,1 but x<1 and not equal to 1, so only value left 1 sufficient (2) x^3 = x \(x^3=x.....x^3x=0......x(x^21)=0\) so x=o or x^2=1 that is 1 and 1 but as seen above only 1 is possible out of 1,0 and 1 sufficient D hi there chetan2u regarding STATEMENT ONE, i dont get how it can be sufficient. This is how i understand it x < 2 When X is positive x < 2 so x can be 1 , 0 , 1 etc now plug in initital question 1^3 < 1^2, > 1<1 TRUE 1^3 < 1^2  > 1<1 NOT TRUE When x is negative x < 2 x < 2 (divide by 1) x > 2 so X can be 1, 0, 1 etc plug in into initial question 1^3 < 1^2  > 1 < 1 TRUE 1^3 < 1^2  > 1 < 1 NOT TRUE So what`s wrong with my approach ? thanks and have a great day



Math Expert
Joined: 02 Aug 2009
Posts: 8023

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
31 Aug 2018, 23:44
dave13 wrote: chetan2u wrote: Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x \(x^3 < x^2.......x^2x^3>0.....x^2(1x)>0\) therefore 1x>0 or x<1 but \(x\neq{0}\) (1) x < 2 so 2<x<2... possible values = 1,0,1 but x<1 and not equal to 1, so only value left 1 sufficient (2) x^3 = x \(x^3=x.....x^3x=0......x(x^21)=0\) so x=o or x^2=1 that is 1 and 1 but as seen above only 1 is possible out of 1,0 and 1 sufficient D hi there chetan2u regarding STATEMENT ONE, i dont get how it can be sufficient. This is how i understand it x < 2 When X is positive x < 2 so x can be 1 , 0 , 1 etc now plug in initital question 1^3 < 1^2, > 1<1 TRUE1^3 < 1^2  > 1<1 NOT TRUE When x is negative x < 2 x < 2 (divide by 1) x > 2 so X can be 1, 0, 1 etc plug in into initial question 1^3 < 1^2  > 1 < 1 TRUE 1^3 < 1^2  > 1 < 1 NOT TRUE So what`s wrong with my approach ? thanks and have a great day look at the colored portion RED and BLUE in red you took x as positive but substituted 1 in the equation and similarly in blue portion, you took x as negative and substituted x as 1 hope you understood
_________________



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1011
WE: Supply Chain Management (Energy and Utilities)

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
01 Sep 2018, 20:28
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) \(x^3=x\) Question stem: x=? Given, x is an integer and \(x^3 < x^2\) Or, \(x^3x^2<0\) Or, \(x^2(x1)<0\) Or,\(x:\:\left(\infty \:,\:0\right)\cup \left(0,\:1\right)\)(a) St1: x < 2Or, 2 < x < 2 Or, x: (2, 2) Or, x={1,0,1}(b) From (a)& (b), the only possible integer value of x=1 (we have an unique value of x) Sufficient. St2: \(x^3=x\) Or, \(x^3x=0\) Or, \(x(x^21)=0\) Or, \(x(x+1)(x1)=0\) x={1,0,1}(c) From (a)& (c), the only possible integer value of x=1 (we have an unique value of x) Sufficient Ans. (D)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior Manager
Joined: 10 Jan 2013
Posts: 302
Location: India
Concentration: General Management, Strategy
GPA: 3.95

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
01 Sep 2018, 22:35
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x chetan2ui have a doubt in the question stem > x^3  x^2 < 0; then x^2  x^3 > 0 x^2(1  x^2) > 0 so since the product is greater than zero, therefore x can never be Zero (right?) secondly, x^2 > 0; x > 0 and 1 > x^2 x < 1 or 1 < x < 1 is this the correct way to break the stem?



SVP
Joined: 26 Mar 2013
Posts: 2340

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
02 Sep 2018, 05:44
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x x^3 < x^2 means 2 things: 1) x does not equal to 0 2) x^2 is always positive, Therefore, we can divide both sides safely by x^2 WITHOUT flipping the sign. It will be if x < 1, Integer x value? (1) x < 2 2< x < 2.........3 intgere values 1, 0 ,1 0 & 1 are invalid values.........So the only integers left is 1........We have unique value Sufficient (2) x^3 = x Refer to note 1 above( zero is not considered), we can divide by x...Hence x^2 =1........Only value is 1 (It can't be 1 as stem says x<1) Sufficient Answer: D



SVP
Joined: 26 Mar 2013
Posts: 2340

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
Updated on: 02 Sep 2018, 05:57
saurabh9gupta wrote: Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x chetan2ui have a doubt in the question stem > x^3  x^2 < 0; then x^2  x^3 > 0 x^2(1  x^2) > 0 so since the product is greater than zero, therefore x can never be Zero (right?) secondly, x^2 > 0; x > 0and 1 > x^2 x < 1 or 1 < x < 1 is this the correct way to break the stem? saurabh9guptaThe part in redis incorrect. x^2(1  x) > 0...It should be x, after factoring out x^2. Also the highlighted part is incorrect x^2 >0 is ok but it is incorrect to conclude that only x > 0 2 > 0 ......2^2 >0 2 <0 ......but also 2^2 >0 So x could take negative or positive value If I continue your way above, I would do the following: x^2 is +ve and does not equal to zero...So divide both sides safely ........So 1 x <.....1<x I hope it helps
Originally posted by Mo2men on 02 Sep 2018, 05:49.
Last edited by Mo2men on 02 Sep 2018, 05:57, edited 1 time in total.



Director
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
02 Sep 2018, 05:56
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x Statemnt I: Given, \(x^2(1x) > 0\).. So, x can be 1,2,3.. etc. But as \(x <2\), x can be only 1.............Sufficient. Statement II: From, this statement  \(x = 0, x = 1\) But x can't be 0 as \(x^2(1x) > 0\). Hence, x = 1Sufficient.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Director
Joined: 24 Nov 2016
Posts: 643
Location: United States

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
15 Oct 2019, 05:20
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x \(x^3<x^2…x=integer…x<0\) (1) x < 2: sufic. \(x<2…2<x<2…(x<0)…2<x<0…x=1\) (2) x^3 = x: sufic. \(x^3=x…x(x^21)=0…x(x+1)(x1)=0…x=(1,0,1)…(x<0)…x=1\) Answer (D)



GMAT Tutor
Joined: 17 Sep 2014
Posts: 207
Location: United States

If x^3 < x^2, what is the value of the integer x?
[#permalink]
Show Tags
15 Oct 2019, 14:51
Bunuel wrote: If x^3 < x^2, what is the value of the integer x?
(1) x < 2 (2) x^3 = x Analyzing the question:x cannot be 0, so \(x^2\) must be positive and we are allowed to divide both sides by \(x^2\). Then the question becomes "If x < 1 what is the value of integer x?" We can continue to list integers that are viable, x = 0 is not in the list so we start from x = 1, 2, 3 etc. Statement 1:This gives 2 < x < 2, combining with x < 1 we get the range of x is 2 < x < 1 and because x is an integer, either x = 1 or x = 0. We also should recall x cannot be 0 so only x = 1 is viable. Sufficient. Statement 2:Move all terms to the left side. \(x^3  x = 0\) can have three solutions at most. Factoring gives \(x*(x+1)(x1) = 0\), so x = 0, x = 1, and x = 1. We can take x= 1 only. Sufficient. Ans: D
_________________
Source: We are an NYC based, inperson and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flatfee tutoring packages, or to publish student score increase rates. Our typical newtoGMAT student score increase rate is 39 points per tutoring hour, the fastest in the world. Feel free to reach out!




If x^3 < x^2, what is the value of the integer x?
[#permalink]
15 Oct 2019, 14:51






