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I do not agree OA and OE. Please provide explanation

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake.
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I do not agree OA and OE. Please provide explanation

Attachment:

math.JPG

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake.

GMAT considers only +ve value for Sqrt()

Sqrt(x) --> lead only one +ve solution.

X^2=4 then both +ve and -ve are valid solutions.
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I marked C first but later I realised that OA should be A.

S1: Suff a. If x=1/4 and y=1/9 >>>> x>y b. If x=9 and y=4 >>>> x>y

S2: X and Y can be +ve or -ve. Insuff.
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I do not agree OA and OE. Please provide explanation

OE is From S1, since X and Y are under a radical, they are nonnegative. So we may safely square them and get . So, S1 is sufficient. According to S2 and can be negative, so we may not insist that

My Question: Why it is assumed that rt(X) is non-negative? If x=4, rt(x) could be +2 /-2.

And based on that answer should be E. Let me know if I am doing any mistake.

Reply:

If you graph the square root of a number then the graph will always be on the positive side. This is a basic principle of math that we learned from pre-calculus course or even earlier. Even Calculus text-book should have them. This is how i see why square root is always positive.

Another way to see this, rt ( -4) doesn't exist because you can not square a number and then get a negative number. I believe that GMAT doesn't want you to break it down from rt(4) to +2/-2. They want you to take it as is. If its rt(4) then you should take it as x=4

You can see the OA by clicking "Reveal" in the spoiler under the question.

RenukaD wrote:

What is the OA?

Thanks dzyubam . my answer was also A but ,looking at posts above, which says "GMAT does not consider -ve values of root" so by this are we trying to say in this case "C" is sufficient condition ? If not then in what scenario we should consider only positive values of roots.

Thanks in advance
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1) X^(1/2) > Y^(1/2) - Because X and Y are under a square-root they can only be positive, or imaginery numbers. thus we can conclude that statment 1 is sufficient.

2) X^2 > Y^2 - This statement tells us that the absolute value of X is greater than Y, but we cannot determine that X is greater than Y, thus this statement is insufficient. For instance: X=3, -3 Y=2, -2

(I) if \sqrt{x}>\sqrt{y} x>y...\sqrt{x} can only be \(>=\) 0 x,y are > 0....hence x > y Sufficient

(II) if x^2 > y^2 x^2 - y^2 >0 (x+y) or (x-y) > 0 both brackets need to be positive or negative.

Both brackets positive: x=4, y= -2; (4-2)(4--2)>0 from here, we have (4-2)(4+2)>0 And x(4) > y.....response is YES sufficient

Both brackets Negative: x=-4; y= -2 (-4 -2) and (-4 +2) from here, we have: (-4-2)(-4+2)>0 And x(-4) < y(-2).....response is NO insufficient So, II is INSUFFICIENT

OA is A. SImply put, test the pair of numbers with different signs: (i) x(4) and y(2) (ii) x(-4) and y(-2) ... and you will realize the insufficiency in II.
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Please elaborate on that. You mean GMAT considers all radical terms positive?

For example, \(\sqrt{4}\) can only be 2, whereas \(x^2=4\) x can be +/- 2?

Then why do we have to keep remembering that the sq rt of something can either be positive or negative?

I know this might come as a source of confusion so let me clarify it well:

The square root symbol means, in fact, the +ve square root of. That's a definition and sometimes we just drop the word "positive" to say simply "the square root of".

Regarding your equation \(x^2=4\) x can be +/- 2, we have 2 answers because of the x^2 and nothing else so that gives 2 answers: one is the positive square root of 4 (which is 2) and the other is the negative of the square root of 4 (which is -2).