If x^3

Question

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

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

chetan2u · Answer

x^3 < x^2.......x^2-x^3>0.....x^2(1-x)>0 therefore 1-x>0 or x<1 but x eq{0} (1) |x| < 2 so -2

SonGoku · Answer

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

combining 1+2

even after clubbing both the statements we have the same result. so the answer must be E.

SonGoku · Answer

Thanks 
 chetan2u 
I have not counted that x not equal to 0 so the answer i got was completely wrong

chetan2u · Answer

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

dave13 · Answer

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

chetan2u · Answer

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

PKN · Answer

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)

saurabh9gupta · Answer

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?

Mo2men · Answer

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

Mo2men · Answer

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

rahul16singh28 · Answer

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.

exc4libur · Answer

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

Answer (D)

TestPrepUnlimited · Answer

Analyzing the question: 
x cannot be 0, so  x^2  must be positive and we are allowed to divide both sides by  x^2 . Since x<1 and x cannot be 0, the question becomes "If x < 0 what is the value of integer x?"

Statement 1: 
 -2 < x < 2, combined with x < 0 we get that the range of x is -2 < x < 0. x=-1. Sufficient.

Statement 2: 
Divide by x.  x^2 = 1  since x<0, x= -1 only. Sufficient.

Ans: D

lakshya14 · Answer

If I divide x^3 by x^2 in the stem, it would give me x<1, then from (1), x = -1 and 0, making (1) insufficient, although without dividing the stem, (A) is sufficient.
Is it that we are dividing the stem because of 0, but in other questions we are getting the correct value with this approach?

bumpbot · Answer

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

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