Let X = -2

[-(-2){-2}]^1/2
2*2^1/2
4^1/2
2

Note: {}=Absolute value


So x = -x

Let X = -2

[-(-2){-2}]^1/2
2*2^1/2
4^1/2
2

Note: {}=Absolute value


So x = -x

But 4^1/2 can be +2 or -2.
hence answer can be +X or -X.

please explain.......

One of the condition is X<0
This rules out +2 and go with -2

You double posted the question....

https://www.beatthegmat.com/algebra-t22735.html

sushanta57021 wrote:Let X = -2

[-(-2){-2}]^1/2
2*2^1/2
4^1/2
2

Note: {}=Absolute value


So x = -x

But 4^1/2 can be +2 or -2.
hence answer can be +X or -X.

please explain.......

4^1/2 is the same as Sqr Rt of 4

sorry for posting it twice, but first i posted it in the wrong forum, i.e DS forum.

But anyway, I am not convinced with the answer yet.
We cann't take -X as answer only because X<0.
let me explain:

Say, P = [-X{abs(X)}]^1/2

is there any reason why P has to be positive? P can be negetive also, that means p can be X.

Can some one please clarify?

well, atleast can some one please tell me whether my logic is right.

I am expecting some answer from you guys.

Thnaks,
Sushanta.

sushanta57021 wrote:sorry for posting it twice, but first i posted it in the wrong forum, i.e DS forum.

But anyway, I am not convinced with the answer yet.
We cann't take -X as answer only because X<0.
let me explain:

Say, P = [-X{abs(X)}]^1/2

is there any reason why P has to be positive? P can be negetive also, that means p can be X.

Can some one please clarify?

Momentarily forget P is positive or negative

we know that x is negative, hence abs(X)=-X

Say, P = [-X{abs(X)}]^1/2

= [-X{-X}]^1/2
= (X^2)^1/2

= square root of ( square of X)

=+ X or -X

But, we know that X is negative no

hence P=-X


( If this is understood, forget what P has to be before calculating and confusion arised from here

when you posted the question in DS, you forgot to mention X <0

Check here

https://www.beatthegmat.com/algebra-t22735.html

hence Logitech said that since outer bracket in solving P is a square root

square root of only positive no is defined

this means he concluded abs(X) was negative

this in turn meant X was negative

This he did since you didnot mention X is negative

Had he known that he would not have done reverse calcns

iamcste wrote:

sushanta57021 wrote:sorry for posting it twice, but first i posted it in the wrong forum, i.e DS forum.

But anyway, I am not convinced with the answer yet.
We cann't take -X as answer only because X<0.
let me explain:

Say, P = [-X{abs(X)}]^1/2

is there any reason why P has to be positive? P can be negetive also, that means p can be X.

Can some one please clarify?

Momentarily forget P is positive or negative

we know that x is negative, hence abs(X)=-X

Say, P = [-X{abs(X)}]^1/2

= [-X{-X}]^1/2
= (X^2)^1/2

= square root of ( square of X)

=+ X or -X

But, we know that X is negative no

hence P=-X


( If this is understood, forget what P has to be before calculating and confusion arised from here

when you posted the question in DS, you forgot to mention X <0

Check here

https://www.beatthegmat.com/algebra-t22735.html

hence Logitech said that since outer bracket in solving P is a square root

square root of only positive no is defined

this means he concluded abs(X) was negative

this in turn meant X was negative

This he did since you didnot mention X is negative

Had he known that he would not have done reverse calcns

P = [-X{abs(X)}]^1/2

Say, X= -2, and can we not write:

(-2) = [-(-2){2}]^1/2

if this equation is true, then P can be X.

Sorry for raising the same question over and over, but believe me I am not convinced yet.
P has to be positive or (-X) as X<0
how come this true

sushanta57021 wrote:sorry for posting it twice, but first i posted it in the wrong forum, i.e DS forum.

But anyway, I am not convinced with the answer yet.
We cann't take -X as answer only because X<0.
let me explain:

Say, P = [-X{abs(X)}]^1/2

is there any reason why P has to be positive? P can be negetive also, that means p can be X.

Can some one please clarify?

Well, i understand your confusion.
But, sqrt(-ve number) gives us a complex number.
Here we are given that x<0.
Lets go according to you,
P = sqrt(-4) assuming x=2, can u get a definite solution for it. No.
So, when we are given x<0, we have to take x as negative and then solve else we cant get answer in the choices mention and complex numbers are indeed out of scope of GMAT land.

I hope your confusion in cleared.....

Rajiv

if you are still confused, please post your detailed solution to this problem as to how are you solving this quetion. May be we can find an error in your approach which you are not able to spot.

Hope it helps

jimmiejaz wrote:

sushanta57021 wrote:sorry for posting it twice, but first i posted it in the wrong forum, i.e DS forum.

But anyway, I am not convinced with the answer yet.
We cann't take -X as answer only because X<0.
let me explain:

Say, P = [-X{abs(X)}]^1/2

is there any reason why P has to be positive? P can be negetive also, that means p can be X.

Can some one please clarify?

Well, i understand your confusion.
But, sqrt(-ve number) gives us a complex number.
Here we are given that x<0.
Lets go according to you,
P = sqrt(-4) assuming x=2, can u get a definite solution for it. No.
So, when we are given x<0, we have to take x as negative and then solve else we cant get answer in the choices mention and complex numbers are indeed out of scope of GMAT land.

I hope your confusion in cleared.....

Rajiv

first of all there is a serious flaw in your explanation. see the highlighted text. i think you didn't get the point of my confusion.
i never considered P = sqrt(-4) assuming x=2
because i know X<0.
let me paraphrase the problem for your better understanding,
can you prove, [-X{abs(X)}]^1/2 >0, given x<0

then only we can get the answer.
anyway thanks for your effort, i really appreciate that, keep up your active participation.

and i could not solve the problem, for me answer can be either +X or -X

we are given p = sqrt(-x|x|) where x<0
lets go by ur approach that soln is +x, it shall satisfy the equation.
p = sqrt(-x.x) since we took the solution as +x
p = sqrt(-x^2)
now, tell me how will you solve this as p = +x?
Hope you get the point now. That if we put the values and backsolve, only -x will give us answer. Hope it helps.

jimmiejaz wrote:we are given p = sqrt(-x|x|) where x<0
lets go by ur approach that soln is +x, it shall satisfy the equation.
p = sqrt(-x.x) since we took the solution as +x
p = sqrt(-x^2)
now, tell me how will you solve this as p = +x?
Hope you get the point now. That if we put the values and backsolve, only -x will give us answer. Hope it helps.

No...your solution does not stand.
I think i explained it earlier.


P = [-X{abs(X)}]^1/2

Say, X= -2, and can we not write:

(-2) = [-(-2){2}]^1/2

if this equation is true, then P can be X.

the highlighted area of your explanation is wrong.
solution is +X does not mean,
p = sqrt(-x.x), solution is +X only means P=+X,
the equation can still be written as
p = sqrt{-(-x).x}
which can give P as +X or -X.