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# Is x positive?

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Math Expert
Joined: 02 Aug 2009
Posts: 7334

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07 Jan 2017, 03:07
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Difficulty:

65% (hard)

Question Stats:

36% (01:15) correct 64% (01:11) wrong based on 101 sessions

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Is x positive?

(1) $$x*|x|=x^2$$

(2) $$x^2*|x|=x^3$$

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

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Status: Long way to go!
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07 Jan 2017, 04:22
chetan2u wrote:
Is x positive?

(1) $$x*|x|=x^2$$

(2) $$x^2*|x|=x^3$$

(1) $$x\times |x| = x^2 \implies x(x-|x|)=0$$

Hence $$x=0$$ or $$x=|x| \implies x \geq 0$$.
In all cases, we have $$x \geq 0$$, insufficient.

(2) $$x^2 \times |x| = x^3 = x^2 \times x \implies x^2 (|x|-x)=0$$

Hence $$x^2=0\implies x=0$$
or $$x=|x| \implies x\geq 0$$
In all cases, we have $$x \geq 0$$. Insufficient.

Combine (1) and (2), we still have $$x \geq 0$$. Insufficient.

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18 Dec 2017, 06:51
chetan2u wrote:
Is x positive?

(1) $$x*|x|=x^2$$

(2) $$x^2*|x|=x^3$$

Very important to NOT miss out all possible values of x- integer, fraction, positive , negative ,0 etc
70% gone wrong means we tend to OVERLOOK 0 as a value..

(1) $$x*|x|=x^2$$
x is surely non-negative BUT it can be 0 or positive
Insuff

(2) $$x^2*|x|=x^3$$
again x can be positive or 0
insuff

combined x can still be o, ans will be NO
x can be positive, ans will be YES
insuff

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

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Joined: 27 Oct 2017
Posts: 1205
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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18 Dec 2017, 07:03
What is the need of considering fraction/integer ?

Statement 1 : it shows that x is non negative, it can be 0 or any positive number.
Statement 2: it shows that x is non negative, it can be 0 or any positive number.
Statement 1 & 2 : it shows that x is non negative, it can be 0 or any positive number.
hence it is not sufficient that x is positive

chetan2u wrote:
chetan2u wrote:
Is x positive?

(1) $$x*|x|=x^2$$

(2) $$x^2*|x|=x^3$$

Very important to NOT miss out all possible values of x- integer, fraction, positive , negative ,0 etc
70% gone wrong means we tend to OVERLOOK 0 as a value..

(1) $$x*|x|=x^2$$
x is surely non-negative BUT it can be 0 or positive
Insuff

(2) $$x^2*|x|=x^3$$
again x can be positive or 0
insuff

combined x can still be o, ans will be NO
x can be positive, ans will be YES
insuff

E

_________________
Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1205
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

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18 Dec 2017, 07:45
you are right, sometimes we make mistakes just because we take x as integers.
Thank you.

chetan2u wrote:
gmatbusters wrote:
What is the need of considering fraction/integer ?

chetan2u wrote:

Very important to NOT miss out all possible values of x- integer, fraction, positive , negative ,0 etc
70% gone wrong means we tend to OVERLOOK 0 as a value..

(1) $$x*|x|=x^2$$
x is surely non-negative BUT it can be 0 or positive
Insuff

(2) $$x^2*|x|=x^3$$
again x can be positive or 0
insuff

combined x can still be o, ans will be NO
x can be positive, ans will be YES
insuff

E

Hi...
The point is general.
Specific to this Q is in colored portion which talks of only 0

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Re: Is x positive?   [#permalink] 18 Dec 2017, 07:45
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