Data Sufficiency

I wanted to understand the difference between X^2 =Y vs x = SQRT(Y),

eg: say x^2 = 36, x can be a +ve 6 or a -ve 6. But if X = SQRT(36), then x = 6 since I beleive that given a SQRT of a number, we can only take positive values. Am I right in making that statement.

In that regard, my question is, if I see a DS question asking for value of x, and if the statements are;

1) x^2 = 36;
2)x = SQRT(36)

Can I safely say, B is SUFFICIENT?


In the same regard, an other flavour of the question is,

Is the value of x + y = 0?

1) xy < 0
2)x^2 = y^2

I appreciate your response.

Ian, can we assume that when an equation looks like, x = SQRT(y^2), it doesn't mean that x= y, but it can be either be y or -y as in |y| ?

x = SQRT(y^2) means x = y. it doest mean x= -y

however if x^2 = y^2, then x = +/- y.


regarding your question

statement 1 : xy < 0 tells that x and y have opp signs. Not suff

statement 2 : x^2 = y^2

(x+y)(x-y) = 0
so either x = - y
or x = y
Not suff

combine both 1 and 2. x = -y so x+y = 0. Suff .. answer C

Ian Stewart wrote:

durgesh79 wrote:x = SQRT(y^2) means x = y. it doest mean x= -y

No, ildude was correct here. If you have the equation x = SQRT(y^2), then x cannot be negative, but y can be negative. So x = |y|. Try this with numbers- let y = -6. Then x will not be equal to y.

yes i agree, Thanks for correcting