priyankur_saha@ml.com wrote:

Is \(X \gt Y\) ?

1. \(\sqrt{X} \gt \sqrt{Y}\)

2. \(X^2 \gt Y^2\)

Source: GMAT Club Tests - hardest GMAT questions

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.

(1): \(X\) and \(Y\) must be both positive. Also, \(\sqrt{X}\) and \(\sqrt{Y}\) are both positive. Squaring the given inequality, we get \(X>Y\).

Sufficient.

Note: If we don't know for sure that both sides of an inequality are positive, we are not allowed to square it. See, for example \(1 > -2\), but \(1 > 4\) is false.

Also, the square root of a positive number is positive (by definition)!

(2) The given inequality can be rewritten as \(X^2-Y^2>0\) or \((X+Y)(X-Y)>0\). The last one states that \(X+Y\) and \(X-Y\) are either both positive or both negative. Therefore, both scenarios \(X > Y\) and \(X < Y\) are possible.

Not sufficient.

Answer: A

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