If x^3 < x^2, what is the value of the integer x? : Data Sufficiency (DS)

SonGoku

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31 Aug 2018, 23:36

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

chetan2u

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31 Aug 2018, 23:39

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SonGoku

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

dave13

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31 Aug 2018, 23:40

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chetan2u

Bunuel

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 what`s wrong with my approach ?

thanks and have a great day

chetan2u

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31 Aug 2018, 23:44

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dave13

chetan2u

Bunuel

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 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

PKN

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01 Sep 2018, 20:28

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Bunuel

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)

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01 Sep 2018, 22:35

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Bunuel

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?

Mo2men

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02 Sep 2018, 05:44

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Bunuel

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

Mo2men

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Updated on: 02 Sep 2018, 05:57

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.

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saurabh9gupta

Bunuel

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

rahul16singh28

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02 Sep 2018, 05:56

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Bunuel

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.

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15 Oct 2019, 05:20

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Bunuel

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.

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

Answer (D)

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15 Oct 2019, 14:51

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Bunuel

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 \(x^2\). 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

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29 Jan 2021, 06:56

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Bunuel

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

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

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?

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