Bunuel wrote:
Official Solution:
The question asks: is \(\frac{x}{y}+\frac{y}{x} \gt 2\)? Or: is \(\frac{x^2+y^2}{xy} \gt 2\)?
Since both unknowns are positive then we can safely multiply by \(xy\):
Is \(x^2+y^2 \gt 2xy\)?
Is \(x^2-2xy+y^2\gt 0\)?
Is \((x-y)^2 \gt 0\)? Now, if \(x\) does not equal \(y\) the answer to this question will be YES, but if \(x=y\), then the answer will be NO, since in this case \((x-y)^2=0\).
(1) \(x\) does not equal \(y\). Directly answers the question. Sufficient.
(2) \(x\) and \(y\) do not share any common divisors except 1. If \(x=y=1\) then the answer is NO, but if \(x=1\) and \(y=2\), then the answer is YES. Not sufficient.
Answer: A
Hello
BunuelAt this step, Is \((x-y)^2 \gt 0\) ?
I went further and arrived at
Is \((x-y) \gt 0\) ?
--> Is \(x \gt y\) ?
Statement 1 says that x not equal to y
Thus x < y or x > y
Hence not sufficient
Statement 2 says that x and y donot share any common divisors except 1
So let x be 2, y be 3 x<y
OR
let x be 3, y be 2 x>y
Hence not sufficient
Option E
Please tell me what is wrong with my approach.
TIA!