If x < 0 , SQRT ( -X |X| ) is equal to

Just check with any negative integer... but i have a doubt...

if x= - 4

SQRT (-(-4). 4) = SQRT 16 which is equal to +- 4... do we take both the values... even if I consider that x<0 we get -4 which is equal to x...

please clarify... thanks...

Adi_Pat wrote:Ques ) If x < 0 , SQRT ( -X |X| ) is equal to

a)-x
b)-1
c)1
d)x
e)|x|

OA A

I didnt get this !!!

Best thing to do is to pick numbers. We are told that x<0 or negative, so lets pick x=-1.

Start with the absolute value to make things easier. l-1l=1. Keep that on the side for now.

Now lets look at -x. Negative of a negative is always positive. In other words -(-1)=1.

so -xlxl=1*1 which is also x^2.

Square root that and you get the real value of x which is -1 or -x because we are told that x<0.

Hope that makes sense.

Hey guys,

Interesting question. Kapur, really good question there...if a question asks you to take a square root and includes the radical sign, it's asking for the positive value. Mainly that's true because, logically, if the GMAT wants you to calculate using that root (say it asks for the value of SQRT 12 + SQRT 27), you can't have +/- values or you'd never get an answer. So for this problem, which asks for the square root and for which you need one value, it's the positive root that they're after.

On the other hand, if a question says that x^2 = 16, you need to know that there are two solutions for x (- and +).

How is that fair?

Well, in the first example, that's how they'll generally ask problem solving questions, for which you need to be able to derive a particular value. For the second, that's the Data Sufficiency variety, in which anything is possible.

They're pretty responsible with those, so don't worry that you're accountable for memorizing arbitrary definitions. Keep in mind that the questions are filtered in the unscored, experimental format, so if an official question is ever too ambiguous in its wording it should be weeded out.


For this question, I'd take issue with the answer choices, as if x is less than 0, then -x should be the same as |x|, so both a and e would be correct.