Gmat prep problems

[Chaitanya_1986]

1) If x<0, then squareroot(-x|x|) is
a) -x b) -1 c) 1 d) x e)squareroot(x)

OA is A)

My approach is

since x<0 take x as -2 then sub in above equation, we get


squareroot(-(-2)|2|)= squareroot(4)= +- 2, since x<0 we get -2

we took x as -2 and we got answer as -2.

So answer is x, but in prep answer is given as A) ....why so????

2) What is the greatest possible area of a triangluar region with one vertex at the center of the circle of radius 1 and the other two vertices on the circle?

a) squareroot(3) / 4 b) 1/2 c) pie/4 d)1 e)squareroot(2)


OA is 1 /2 i.e B

[rros0770]

(1) The example you presented is correct, up until:

"= squareroot(4)= +- 2"

On the GMAT, anything under a square root sign must yield a positive value. Negative Square roots are imaginary numbers and are outside the scope of the GMAT.

Therefore squareroot(4) simply yields a positive value of 2

Using your example, when -2 is inserted into the equation "squareroot(-x|x|)", the output is 2. Therefore the answer is (A) -X

[manpsingh87]

1) If x<0, then squareroot(-x|x|) is
a) -x b) -1 c) 1 d) x e)squareroot(x)

x<0; sqrt(-x|x|);
as x<0; therefore |x|=-x;
sqrt(-x(-x)); sqrt(x^2); now this can be equal to either x or -x, but since x<0; therefore answer should be -x..!!!

[pemdas]

1) If x<0, then squareroot(-x|x|) is
a) -x b) -1 c) 1 d) x e)squareroot(x)

let's work through inequality condition and disallow x=0 (x is not equal to 0), √(-x*|x|)>0 as the negative root of numbers is not allowed in GMAT (according to GMAT conventions, it's allowed in MATH as a whole) -x*|x|>0 is possible only if x<0 because |x| is positive and -x multiplied by positive number will be less than 0. Therefore x must be negative, x<0. We agreed that √number cannot be negative in GMAT, hence √(-x*|x| is valid only with -x.