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.
Difference between square root/square
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Technically, in math-speak, we say that the square root symbol gives the "non-negative square root", (and not the 'positive root') because the result might be equal to zero (which only happens if you take the SQRT of zero). If you see the square root symbol -- which you see in many GMAT questions -- that symbol means 'the non-negative square root'; SQRT(36) is equal to 6. But, as you point out, if x^2 = 36, all you can say is that x = 6 or x = -6; there's no way to find an exact value for x.ildude02 wrote: 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.
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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
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
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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.durgesh79 wrote:x = SQRT(y^2) means x = y. it doest mean x= -y
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yes i agree, Thanks for correctingIan Stewart wrote: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.durgesh79 wrote:x = SQRT(y^2) means x = y. it doest mean x= -y