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by rohit_gmat » Sun Nov 21, 2010 6:07 am
Please help with this question.... the way i see it, it needs imaginary numbers (i/j) ... but as per my knwledge, this aint tested on the gmat....


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by Geva@EconomistGMAT » Sun Nov 21, 2010 6:14 am
rohit_gmat wrote:Please help with this question.... the way i see it, it needs imaginary numbers (i/j) ... but as per my knwledge, this aint tested on the gmat....


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1) No imaginary numbers needed: since x is negative, -x becomes positive. Since the absolute value is always non-negative, the result of -x|x| is the product of two positive numbers, and the root is taken correctly.

2) However, the question is indeed confusing. Since the answer choices include x, avoid the confusion by plugging in a negative value of x, such as x=-2. If x=-2, then sqrt ( -(-2)|-2|_ = sqrt (2*2) = sqrt(4) = 2. Thus, if we plug in x=-2 into the answer choices, the right answer should equal -2: Eliminate all other answer choices which do not match this goal. Doing this helps you see that the answer is A -(-2)=2, and not D x=-2, which is the strongest trap answer.

While not necessarily faster than algebra (though it can be), plugging in and eliminating is usually the safer way to solve a question with variables in answer choices. The mistakes you are likely to make dealing with abstract algebraic concepts , you are far less likely to do when using real numbers you can wrap your head around. At the end of the day, we choose A not because we have proven that A is the right answer choices algebraically, but rather because none of the other answer choices match our goal, and we know that one answer choice in 5 must be correct: since we've eliminated four answer choices, the last one must be the correct one, and we needn't worry about why.
Last edited by Geva@EconomistGMAT on Sun Nov 21, 2010 6:19 am, edited 1 time in total.
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by Rahul@gurome » Sun Nov 21, 2010 6:15 am
rohit_gmat wrote:Please help with this question.... the way i see it, it needs imaginary numbers (i/j) ... but as per my knwledge, this aint tested on the gmat....

If x < 0, then √(-x|x|) is
  • (A) -x
    (B) -1
    (C) 1
    (D) x
    (E) √x
Don't worry.
This doesn't need any imaginary number concept! :)

As x < 0, |x| = -x.
Thus √(-x|x|) = √[(-x)*(-x)] = √(x²) = |x| = -x

The correct answer is A.
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by rohit_gmat » Sun Nov 21, 2010 6:29 am
damnnnnnnnnn... i totally didnt see that... i even plugged in n then picked "x" :P

thank u alll & plz pray for me !! :)

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by Geva@EconomistGMAT » Sun Nov 21, 2010 6:57 am
Best of luck!
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by rohit_gmat » Sun Nov 21, 2010 9:31 am
Thanks !!!!


BTW OA is A
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by purnimaksingh » Tue Nov 23, 2010 12:06 pm
rohit_gmat wrote:damnnnnnnnnn... i totally didnt see that... i even plugged in n then picked "x" :P

thank u alll & plz pray for me !! :)

BTG rocks!!
One t hing I didnt unederstand mod[x]=sqrt[x] how is that
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by purnimaksingh » Tue Nov 23, 2010 12:07 pm
rohit_gmat wrote:damnnnnnnnnn... i totally didnt see that... i even plugged in n then picked "x" :P

thank u alll & plz pray for me !! :)

BTG rocks!!
One t hing I didnt unederstand mod[x]=sqrt[x] how is that
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by goyalsau » Tue Nov 23, 2010 6:08 pm
purnimaksingh wrote:
One t hing I didnt unederstand mod[x]=sqrt[x] how is that
If x < 0, then √(-x|x|) is

(A) -x
(B) -1
(C) 1
(D) x
(E) √x[/list][/quote]

I think it better to solve it with assuming a value of x , I know the solution provided by Rahul is the Shortest But it is the shortest but assuming value for x will be good too,

Lets x = -2

√(-x|x|) = √(-(-2)|-2|)
√(2 * 2)
= 2

x = - 2

- x = - ( - 2 ) , - x = 2

But Root will always have two values one is +ve and other one is -ve

Why we are not considering the negative value
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by mk101 » Tue Nov 23, 2010 6:26 pm
goyalsau wrote:
purnimaksingh wrote:
One t hing I didnt unederstand mod[x]=sqrt[x] how is that
If x < 0, then √(-x|x|) is

(A) -x
(B) -1
(C) 1
(D) x
(E) √x[/list]
I think it better to solve it with assuming a value of x , I know the solution provided by Rahul is the Shortest But it is the shortest but assuming value for x will be good too,

Lets x = -2

√(-x|x|) = √(-(-2)|-2|)
√(2 * 2)
= 2

x = - 2

- x = - ( - 2 ) , - x = 2

But Root will always have two values one is +ve and other one is -ve

Why we are not considering the negative value [/quote]

<b>



The answer lies in the way squareroot function is defined.

Y =SQ ROOT(x) SUCH that x and y are both positive numbers.

In our case x = x^2 (this must be positive) and the evaluation , i.e. "y" is positive as well. </b>
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by goyalsau » Tue Nov 23, 2010 6:36 pm
I know it may sound stupid , But i am not able to understand a word of it, Please explain it in simple language..... :(
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by mk101 » Tue Nov 23, 2010 6:47 pm
any relation of the form y = squareroot(x) is called as a square root function.....Any function is a relation between two variables. in this case the two variables are x and y.

In our case we have y = squareroot of (x^2).

The basic definition of the squareroot function says - "the function is defined only for positive values of x^2 and y".

Hence whenever we take the squareroot of a function of the form y = squareroot (x^2) , we need to consider only the positive square root of x ^2.

I hope that explains your query.
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by goyalsau » Tue Nov 23, 2010 6:54 pm
mk101 wrote:any relation of the form y = squareroot(x) is called as a square root function.....Any function is a relation between two variables. in this case the two variables are x and y.

In our case we have y = squareroot of (x^2).

The basic definition of the squareroot function says - "the function is defined only for positive values of x^2 and y".

Hence whenever we take the squareroot of a function of the form y = squareroot (x^2) , we need to consider only the positive square root of x ^2.

I hope that explains your query.
Many Thanks,
I didn't know that, But as you its only for variables , Where y = square root of x ^ 2
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