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

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Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 11:46
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Difficulty:

45% (medium)

Question Stats:

54% (00:46) correct 46% (01:01) wrong based on 364 sessions

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Is $$x > 0$$?

1. $$x^2 = 9x$$
2. $$|x| = -x$$
Math Expert
Joined: 02 Aug 2009
Posts: 7104
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 19:27
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
_________________

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

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Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 21:00
1
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.
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Math Expert
Joined: 02 Aug 2009
Posts: 7104
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 21:07
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
_________________

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

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Joined: 03 Dec 2014
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 21:10
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
Joined: 02 Sep 2009
Posts: 51121
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 21:11
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
Joined: 02 Aug 2009
Posts: 7104
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 21:13
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
_________________

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

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 51121
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

### Show Tags

07 Apr 2016, 21:13
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.
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Joined: 16 Mar 2016
Posts: 3
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 22:26
Why the first option is not enough?

we have: x^2=9x if we divide both sides for x we have x=9 .
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Joined: 02 Sep 2009
Posts: 51121
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Apr 2016, 22:30
andreroma wrote:
Why the first option is not enough?

we have: x^2=9x if we divide both sides for x we have x=9 .

Please read this solution. You'll see that TWO solutions satisfy x^2=9x: x= 0 and x = 9. You cannot divide both parts by x because x can be 0 and you cannot divide by 0.
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Location: India
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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11 Jun 2017, 08:59
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?
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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11 Jun 2017, 23:31
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.

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.
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Posts: 121
Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Oct 2018, 06:53
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
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Oct 2018, 12:12
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.
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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07 Oct 2018, 20:34
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.
Re: Is x > 0? x2 = 9x |x| = -x &nbs [#permalink] 07 Oct 2018, 20:34
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