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

 It is currently 23 Oct 2019, 11:20

### 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

# If x^3 < x^2, what is the value of the integer x?

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
1
2
00:00

Difficulty:

85% (hard)

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

_________________
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
1
Bunuel wrote:
If x^3 < x^2, what is the value of the integer x?

(1) |x| < 2
(2) x^3 = x

$$x^3 < x^2.......x^2-x^3>0.....x^2(1-x)>0$$
therefore 1-x>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
$$x^3=x.....x^3-x=0......x(x^2-1)=0$$
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
GMAT 1: 460 Q42 V14
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^3-x^2<0
x^2(x-1)<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^3-x=0
x(x^2-1)=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
GMAT 1: 460 Q42 V14
If x^3 < x^2, what is the value of the integer x?  [#permalink]

### Show Tags

31 Aug 2018, 23:36
Thanks
chetan2u
I 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
chetan2u
I 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

$$x^3 < x^2.......x^2-x^3>0.....x^2(1-x)>0$$
therefore 1-x>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
$$x^3=x.....x^3-x=0......x(x^2-1)=0$$
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 whats 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
1
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

$$x^3 < x^2.......x^2-x^3>0.....x^2(1-x)>0$$
therefore 1-x>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
$$x^3=x.....x^3-x=0......x(x^2-1)=0$$
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 whats 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, $$x^3-x^2<0$$
Or, $$x^2(x-1)<0$$
Or,$$x:\:\left(-\infty \:,\:0\right)\cup \left(0,\:1\right)$$-------------(a)

St1:- |x| < 2
Or, -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, $$x^3-x=0$$
Or, $$x(x^2-1)=0$$
Or, $$x(x+1)(x-1)=0$$
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
1
Bunuel wrote:
If x^3 < x^2, what is the value of the integer x?

(1) |x| < 2
(2) x^3 = x

chetan2u

i 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

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

chetan2u

i 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?

saurabh9gupta

The 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
GMAT 1: 700 Q50 V33
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, $$x^2(1-x) > 0$$.. 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 $$x^2(1-x) > 0$$. Hence, x = -1

Sufficient.
_________________
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.

$$x^3=x…x(x^2-1)=0…x(x+1)(x-1)=0…x=(-1,0,1)…(x<0)…x=-1$$

GMAT Tutor
Joined: 17 Sep 2014
Posts: 207
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
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 $$x*(x+1)(x-1) = 0$$, so x = 0, x = -1, and x = 1. We can take x= -1 only. Sufficient.

Ans: D
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 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
Display posts from previous: Sort by