GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 Apr 2018, 19:15

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is x positive?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 5774

### Show Tags

07 Jan 2017, 04:07
00:00

Difficulty:

65% (hard)

Question Stats:

38% (00:43) correct 62% (00:40) wrong based on 94 sessions

### HideShow timer Statistics

Is x positive?

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

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

[Reveal] Spoiler: OA

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Senior CR Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1368
Location: Viet Nam

### Show Tags

07 Jan 2017, 05:22
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.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5774

### Show Tags

18 Dec 2017, 07:51
Expert's post
1
This post was
BOOKMARKED
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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Senior Manager
Joined: 27 Oct 2017
Posts: 313
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

### Show Tags

18 Dec 2017, 08:03
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

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts

Appreciate my post by giving kudos .

Senior Manager
Joined: 27 Oct 2017
Posts: 313
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)

### Show Tags

18 Dec 2017, 08:45
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

_________________

SC: Confusable words
All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts

Appreciate my post by giving kudos .

Re: Is x positive?   [#permalink] 18 Dec 2017, 08:45
Display posts from previous: Sort by