Choice 1 says that x has to be negative.

so suppose x = -1

-(-1)*|-1| > 0

so[ (-6)^2 ] ^ (1/2) = 36^(1/2) = 6 which equals 5 - (-1)

So choice 1 is sufficient.

Choice 2 states that x has to be a number less than 5.

so we can pick x = 3

[(3-5)^2]^(1/2) = (-2)^2 = 4^(1/2) = 2 which equals 5 - 3 = 2

So Choice 2 is also sufficient.

Therefore it is D

hey ssmiles...why didnt you take 36^1/2= +6 or -6 ?

i could solve this ques using stmt 1. but as PAB asked why are we not takin root of a no. as -??

(-2^2)^0.5 --> -2
and 5-3 = 2??

The question asks if sqrt(x-5)2 = 5-x
GMAT refers to all given sqrt values as +ve values, and if this is true then the question translates to Is 5-x > 0
(Note: I am NOT a 100% if this is TRUE here, it if is then it is a piece of cake)

1. -x|x| > 0
|x| is always positive, so for the above to be positive -x should be positive, i.e. x is negative
If x is negative, then 5>x or 5-x>0
Sufficient

2. 5-x > 0 is what is being asked hence Sufficient.

Answer: D

in this question you can use the following equivalence
(x ^ 2) ^(1/2) = |X| and therefore ((x-5)^2)^(1/2) = |X-5|

rephrasing the question is |X-5| = 5 - X?

now split the absolute value in intervals
X > 5 |X-5| = X -5 which is not equal to 5 - X
0 < X < 5 |X-5| = 5 -X which is equal to 5 - X
X < 0 |X-5| = 5 + X because X is negative the expression is
|X-5| = 5 - (-X) ---> 5 + X = 5 + X true
so the expression is true for X<=5

now take the statements
1 ) X is negative so the expression is true sufficient
2 ) X < 5 the expression is true sufficient.

PAB2706 wrote:hey ssmiles...why didnt you take 36^1/2= +6 or -6 ?

sorry way late reply here...I am sure the others have cleared up the doubts.

but essentially, when you take a square root of a number, the result is always positive, otherwise it results in a complex number.

I think we always see a number such as x^2 = 36 and x = (-6)^2 or (6)^2 but the reverse process(^1/2) only holds true for positive values

Thanks a lot everyone...

(x ^ 2) ^(1/2) = |X| --- this is really helped...

Thanks a lot everyone...

(x ^ 2) ^(1/2) = |X| --- this is really helped...