Data Sufficiency (DS) | Re: If x, y, and z are positive integers, where x > y and z = √x

It is given that x and y are 2 consecutive squired. This means they are squires of 2 integers whose mod will give 2 consecutive integers.

Let

x =\(n^2\)
y =\((n-1)^2\) As x > y

Option 1

x+y =8z+1 =>\(n^2\) +\((n-1)^2\) = 8n+1 =>2\(n^2\) - 2n +1 = 8n +1 =>\(2n^2\) - 10n=0 => n=0,5
The equation satisfied for 2 values of n, while for other values of n it do not satisfy.
Hence, INSUFFICIENT

Option 2

x-y = 2n-1 =>\(n^2\) -\((n-1)^2\) = 2n-1 =>\(n^2\) - (\(n^2\) +1 -2n)
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