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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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New post 07 Apr 2016, 12:46
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Is \(x > 0\)?

1. \(x^2 = 9x\)
2. \(|x| = -x\)
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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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
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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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New post 07 Apr 2016, 22:00
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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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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

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

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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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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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
_________________

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

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

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

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New post 07 Apr 2016, 23:30
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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Collection of Questions:
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Re: Is x > 0? x2 = 9x |x| = -x  [#permalink]

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

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

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

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

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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.
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Re: Is x > 0? x2 = 9x |x| = -x &nbs [#permalink] 07 Oct 2018, 21:34
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