priyankur_saha@ml.com wrote:

Is

X \gt Y ?

1.

\sqrt{X} \gt \sqrt{Y} 2.

X^2 \gt Y^2Source: 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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