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(1) |y|> 1. Probably the easiest way to deal with this statement would be to plug some numbers. Notice that \(|y|> 1\) means that \(y<-1\) or \(y>1\). Now, if \(y=2\) and \(x=-4\) then the answer is YES but if \(y=-2\) and \(x=4\) then the answer is NO. Not sufficient.

(2) |x| < 3 --> \(-3<x<3\): directly gives an YES answer to the question. Sufficient.

From the question: xy<3 => x,y can be both positive and negative or, opposite signs. x(-2)y(3)<3 1. |y| > 1 => y>1 y<-1 => y can take 2, 3, 4, 5 or -2, -3, -4, -5.. if y=-6 and x=6 xy is -36 <3. If y=-1, x=-2 xy<3. here x = 6 in one case and -2 in another case. Hence Insufficient. 2. |x|<3 => -3<x<3 . No matter what the values of x are, it will be <3. Sufficient.
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