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Some questions from GMAT Prep - please help

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Some questions from GMAT Prep - please help

by momentary_lapse » Sat Mar 24, 2007 9:39 pm
1) If x<0 , what is square root of -x|x|

I thought if x<0, |x| = -x
THerefore square root becomes the root of x^2 which is + or - x

I wrote the answer as x but the GMAT Prep says that answer is -x. How???

2) Data Sufficiency:

Is 1/p > r/(r^2 + 2)

1) p=r
2) r=0

Please help with this too

Thanks a lot in advance!
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Re: Some questions from GMAT Prep - please help

by dsuna » Sun Mar 25, 2007 8:58 am
momentary_lapse wrote:1) If x<0 , what is square root of -x|x|

I thought if x<0, |x| = -x
THerefore square root becomes the root of x^2 which is + or - x

I wrote the answer as x but the GMAT Prep says that answer is -x. How???

2) Data Sufficiency:

Is 1/p > r/(r^2 + 2)

1) p=r
2) r=0

Please help with this too

Thanks a lot in advance!
1.) X<0, let's say x= -2, then square root of -x|x| = square root of -(-2)*|-2| = square root of -(-2)(-2) =square root of -4 = -2, hence solution is -x

2.) is the answer D?

r^2+2 > pr
r^2-pr+2>0

1. p=r then r^2-r^2+2>0, 2>0, sufficient
2. r=0 then 0-0+2>0, 2>0, sufficient

the answer should be D
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Re: Some questions from GMAT Prep - please help

by jayhawk2001 » Sun Mar 25, 2007 9:55 am
For question 2 --

1 - insufficient. For p = r = 2, we have 1/2 > 1/3 which is true.
For p = r = -2, we have -1/2 > -1/3 which is not true.

2 - insufficient. We just have 1/p > 0

Combining 1 and 2, we have p = r = 0 which leads us nowhere.

Is it E ?
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by aim-wsc » Sun Mar 25, 2007 12:47 pm
give one more try @DS guys ;)
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by momentary_lapse » Sun Mar 25, 2007 6:31 pm
The answer to 2 is C. The first equation is insufficient since the inequality sign will change based on negative and positive values of r. The second one makes it clear by saying that r is +ve and p=r i.e. the equation will hold good.

For the first one, if x = -2 then suare root of -x|x| = -(-2)|-2|
which is = 2|-2| = 2*2 = 4 and square root is + or -2 .

How can the square root of a negative number be a negative number. It should be imaginery.
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by momentary_lapse » Sun Mar 25, 2007 6:35 pm
However the GMAT prep gave the options as -x,x,1,0 and square root of x. The answer is also supposed to be -x. How?? I just cant figure it out.
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by aim-wsc » Sun Mar 25, 2007 7:10 pm
present the original answer, what GMATprep has to say.
and do check the announcement made at sub-forums.
Thanks for the patience. explanation
is on the way :)
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by jayhawk2001 » Sun Mar 25, 2007 7:48 pm
[quote="momentary_lapse"]The answer to 2 is C. The first equation is insufficient since the inequality sign will change based on negative and positive values of r. The second one makes it clear by saying that r is +ve and p=r i.e. the equation will hold good.

[/quote]

Hmm, (2) just leads to 1/p > 0. However, if you combine
1 and 2, you get p = r = 0.

One can't cross-multiply this inequality when p = r = 0.
1/p > r/(r^2 + 2)

The question hence boils down to the following
Is 1/ 0 > 0 / (0 + 2)

I'm still not fully convinced that C is the correct answer but I guess
GMAT Prep answer is the final answer :-)
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Re: Some questions from GMAT Prep - please help

by Neo2000 » Sun Mar 25, 2007 11:50 pm
momentary_lapse wrote:1) If x<0 , what is square root of -x|x|

I thought if x<0, |x| = -x
THerefore square root becomes the root of x^2 which is + or - x
You were fine till here. Then since we said in the very beginning that X<0
solution set CANNOT contain +X
Therefore your answer is -X
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by momentary_lapse » Mon Mar 26, 2007 8:28 am
Neo,

If x = -2 then the square root of X^2 is + or -2 right? Because x^2 is 4 and whether x is < 0 or > 0 the square root of a +ve number can be either the +ve root or the -ve root.

What does the value of x have to do with this? Lets say x=-2, then the answer is -x which is -(-2) = 2. This defeats the reasoning you are giving saying that x < 0 therefore the answer should be -x.
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by Neo2000 » Mon Mar 26, 2007 9:11 am
momentary_lapse wrote:Neo,

If x = -2 then the square root of X^2 is + or -2 right? Because x^2 is 4 and whether x is < 0 or > 0 the square root of a +ve number can be either the +ve root or the -ve root.
Yup the root can be either positive or negative. However, since we said X is <0 then we cannot have a value of X>0 which means the answer has to be -2
momentary_lapse wrote: What does the value of x have to do with this? Lets say x=-2, then the answer is -x which is -(-2) = 2. This defeats the reasoning you are giving saying that x < 0 therefore the answer should be -x.
My reasoning was as follows
Modulus function always give the positive value/max value/magnitude of X

Since X<0, value of X is negative say -y
Then -(-y)|-y|
= y(y) = y^2

So square root of this becomes +or- y
However we've already said that X<0 which means X cannot have a positive value so the value has to be -y
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by gabriel » Mon Mar 26, 2007 9:36 am
jayhawk2001 wrote:
Hmm, (2) just leads to 1/p > 0. However, if you combine
1 and 2, you get p = r = 0.

One can't cross-multiply this inequality when p = r = 0.
1/p > r/(r^2 + 2)

The question hence boils down to the following
Is 1/ 0 > 0 / (0 + 2)

I'm still not fully convinced that C is the correct answer but I guess
GMAT Prep answer is the final answer :-)
jay u r right according to the given statements... the answer shuld be E... even if both the staements are combined we wuld get ( as already stated by u ).... 1/0 and 0/ ( 0+2 )... and 1/0 is mathematically not defined....

the second statment is actually r>0.... by using this we get the answer as C...
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by gabriel » Mon Mar 26, 2007 10:53 am
momentary_lapse wrote:However the GMAT prep gave the options as -x,x,1,0 and square root of x. The answer is also supposed to be -x. How?? I just cant figure it out.

Ok.. the q asks to find the sq root ( -x mod (x))= sq root ( -x )* sq root ((mod(x)) = sq root (-x)* sq root(-x)... let this be eqn no. 1....

.. for understanding this u need to know the basics of complex numbers... the root of a negative qty -x can be written as sqroot (x)* sqroot (-1)... so applying this to eqn 1.... we get sqroot (x)*sqroot(-1) * sqroot(x)*sqroot(-1) .... that is sqroot (x)*sqroot(x)*sqroot(-1)*sqroot(-1)... which is equal to -x...

so basically sqroot ( (-x)^2) = -x..... similarly sqroot (-a) * sqroot(-b) is not equal to sqroot(ab)... but is equal to - sqroot(ab)... hope this helps...
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by momentary_lapse » Tue Mar 27, 2007 11:00 am
Well the questions says square root of (-x|x|) where x<0

So it seems to be asking for the square root of the product of -x and |x|

Im not sure how square root of (-x)(-x) is -x

Which property of complex numbers is this?
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by aim-wsc » Tue Mar 27, 2007 11:37 am
gabriel wrote:

Ok.. the q asks to find the sq root ( -x mod (x))= sq root ( -x )* sq root ((mod(x)) = sq root (-x)* sq root(-x)... let this be eqn no. 1....

.. for understanding this u need to know the basics of complex numbers... the root of a negative qty -x can be written as sqroot (x)* sqroot (-1)... so applying this to eqn 1.... we get sqroot (x)*sqroot(-1) * sqroot(x)*sqroot(-1) .... that is sqroot (x)*sqroot(x)*sqroot(-1)*sqroot(-1)... which is equal to -x...

so basically sqroot ( (-x)^2) = -x..... similarly sqroot (-a) * sqroot(-b) is not equal to sqroot(ab)... but is equal to - sqroot(ab)... hope this helps...
wow!
but dont make it complex by bringing complex numbers here! :lol:
even by hearing the word I almost got an heart attack there ;)


OK let me try 8)
1) If x<0 , what is square root of -x|x|

I thought if x<0, |x| = -x
THerefore square root becomes the root of x^2 which is + or - x

I wrote the answer as x but the GMAT Prep says that answer is -x. How???
first off: |x| CANNOT BE equal to -x (never)

now -x|x| = (-1)* (x) * mod (x).............(remember x has -ve value already! since x<0) so let x= (-1)* x' where x'= (+ve) x

=(-1)* (-1)x' * x'
= (-1)^2 * x'^2
I think it is very easy to sq rooting above value.
which equals to =(-1)* x'
=-x
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