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

It is currently 17 Oct 2019, 18:22

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is x > 0? x2 = 9x |x| = -x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
User avatar
S
Joined: 18 Sep 2014
Posts: 1093
Location: India
GMAT ToolKit User Reviews Badge
Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 12:46
1
16
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

55% (01:02) correct 45% (01:11) wrong based on 400 sessions

HideShow timer Statistics

Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7971
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 20:27
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)



Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58402
Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:00
1
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7971
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:07
Bunuel wrote:
chetan2u wrote:
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)



Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B


Notice that for (2) x can be 0 too. The rest is correct.


hi,
I too thought of x as 0 or -ive ..
but since we are answering "is x>0?"
Ans will be NO in both cases and went with B
_________________
Manager
Manager
avatar
B
Joined: 03 Dec 2014
Posts: 91
Location: India
Concentration: General Management, Leadership
GMAT 1: 620 Q48 V27
GPA: 1.9
WE: Engineering (Energy and Utilities)
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:10
chetan2u wrote:
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)



Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B



But X=0 is true, then can we say stmt 2 is sufficient.?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58402
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:11
chetan2u wrote:
Bunuel wrote:
chetan2u wrote:

Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B


Notice that for (2) x can be 0 too. The rest is correct.


hi,
I too thought of x as 0 or -ive ..
but since we are answering "is x>0?"
Ans will be NO in both cases and went with B


Yes, B is correct. I just pointed out that \(|x| = -x\) means that \(x \leq 0\), not x < 0.
_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7971
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:13
robu wrote:
chetan2u wrote:
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)



Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B



But X=0 is true, then can we say stmt 2 is sufficient.?



Yes statement 2 will be suff in both cases..
1) if x=0..
Q is " is x>0?"----ans -NO

2) x is -ive
Q is " is x>0?"----ans -NO

so both cases ans is NO
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58402
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 22:13
robu wrote:
chetan2u wrote:
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)



Hi,

lets see the statements


1. \(x^2 = 9x\)..
\(x^2 - 9x = 0\)..
\(x(x-9)=0\)..
so x=0 or x=9...
Insuff

2. \(|x| = -x\)
this shows -x is +ive , so x has to be -ive
ans is NO

Suff

B



But X=0 is true, then can we say stmt 2 is sufficient.?


From (2) x can be 0 or negative. In any case answer to the question is x > 0 is NO, thus sufficient.
_________________
Intern
Intern
avatar
Joined: 16 Mar 2016
Posts: 3
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 23:26
Why the first option is not enough?

we have: x^2=9x if we divide both sides for x we have x=9 .
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58402
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Apr 2016, 23:30
Current Student
avatar
G
Joined: 19 Aug 2016
Posts: 146
Location: India
GMAT 1: 640 Q47 V31
GPA: 3.82
Reviews Badge
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 11 Jun 2017, 09:59
Bunuel wrote:

Yes, B is correct. I just pointed out that \(|x| = -x\) means that \(x \leq 0\), not x < 0.


Hi,

I have a difficulty understanding the second statement. Anything inside mod is positive right so how is that equal to a negative number? Can you please elaborate on this?
_________________
Consider giving me Kudos if you find my posts useful, challenging and helpful!
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 12 Jun 2017, 00:31
ashikaverma13 wrote:
Bunuel wrote:

Yes, B is correct. I just pointed out that \(|x| = -x\) means that \(x \leq 0\), not x < 0.


Hi,

I have a difficulty understanding the second statement. Anything inside mod is positive right so how is that equal to a negative number? Can you please elaborate on this?


Hi

Anything inside mod is NOT necessarily positive. However, anything that comes out of mod (as a result) is either positive or zero.
Please consider the following:

1) Let x = 5. Here |x| = 5. So the number inside mod is positive, and the result is also positive. We can see here that |x| = x only.

2) Let x = 0. Here |x| = 0. So the number inside mod is zero, and the result is also zero. We can see here that |x| = x, OR we can also say that |x| = -x, because putting a negative sign before 0 also is 0 only.

3) Let x = -4. Here |x| = 4. Here the number inside mod is negative, BUT the result is positive, which is actually negative of that negative number.
I mean -(-4) = 4. We can see here that |x| = 4 = -(-4) = -x.

So if we are given that |x| = -x, it could mean two things: Either x is 0, Or x is negative. That is what Bunuel wrote in his comment.
Manager
Manager
User avatar
G
Joined: 01 Jan 2018
Posts: 154
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Oct 2018, 07:53
Hello chetan2u,
I couldnt understand the first condition, please explain why we cant consider 9X>0, as x^2 will always be +ve.

Regards,
Tamal
_________________
kudos please if it helped you.
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Oct 2018, 13:12
Nevernevergiveup wrote:
Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)

\(x\,\,\mathop > \limits^? \,\,0\)

\(\left( 1 \right)\,\,{x^2} = 9x\,\,\,\, \Leftrightarrow \,\,\,\,x\left( {x - 9} \right) = 0\,\,\,\, \Leftrightarrow \,\,\,\,\left\{ \matrix{
\,x = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr
\,\,\,{\rm{OR}} \hfill \cr
\,x = 9\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.\)

\(\left( 2 \right)\,\,\,\left| x \right| = - x\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \le 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1428
Location: India
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

Show Tags

New post 07 Oct 2018, 21:34
tamal99 wrote:
Hello chetan2u,
I couldnt understand the first condition, please explain why we cant consider 9X>0, as x^2 will always be +ve.

Regards,
Tamal


Hello

Its NOT necessary that x^2 will be positive only, x^2 can be 0 also (if x is 0). So we have to consider that possibility also for first statement.
GMAT Club Bot
Re: Is x > 0? x2 = 9x |x| = -x   [#permalink] 07 Oct 2018, 21:34
Display posts from previous: Sort by

Is x > 0? x2 = 9x |x| = -x

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne