What is the source of this question. PS: OA means official answer.

I am not sure if this is a GRE question.

THIS IS A BAD QUESTION.condition 1:

x+y>3condition 2: \(x^{2}-y^{2}< 8\)

We start by picking numbers. So the difference between squares has to be less than 8.

condition 1:

x+y>3condition 2: \(x^{2}-y^{2}< 8\)

For example 1,3 now \(3^2-1^2 = 8\) and \(3+1=4\) condition 1 is statisfied condition 2 is not.

Next pair is 3,4. So \(4^2-3^2 = 7\) and and \(3+4=7\). This satisfies but this may not be the gratest value of x. Try the next pair. 5,4

\(5^2-4^2 = 9\) SO not true.

\(6^2-5^2 = 11\)

\(7^2-6^2 = 13\)

Note that the difference between consecutive squares keep on increasing. So 3,4 is the only viable pair.

HERE is why this is a BAD question. \(y>x\).

Say y=1000 x=500.

\(x+y =1500\) holds

\(x^2-y^2=-750000 < 8\) holds

Now here x can have infinitely many values. x=1 and y=1000 holds so does x=999 and y=1000. Also y can have any value.

_________________

Sandy

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