Princ wrote:
If \(a\) and \(b\) are positive integers and \(a > b\), what is the remainder when \(a^2 - 2ab + b^2\) is divided by \(9\)?
(1) The remainder when \(a-b\) is divided by \(3\) is \(2\).
(2) The remainder when \(a-b\) is divided by \(9\) is \(2\).
From question stem it is asking for \(\frac{(a-b)^2}{9}\)
Statement 1) \(\frac{(a-b)}{3} = q + \frac{2}{3}\) this can be converted to \(a-b = 3q + 2\)
if q = 0 then a-b = 2 and \((a-b)^2\) = 4 as a result it is 4/9
if q = 1 then a-b = 5 and \((a-b)^2\) = 25 as a result it is \(\frac{25}{9} = 2 \frac{7}{9}\)
Insufficient.
Statement 2) \(\frac{(a-b)}{9} = q + \frac{2}{9}\) this can be converted to \(a-b = 9q + 2\)
if q = 0 then a-b = 2 and \((a-b)^2\) = 4 as a result it is 4/9
if q = 1 then a-b = 11 and \((a-b)^2\) = 121 as a result it is \(\frac{121}{9} = 13 \frac{4}{9}\)
Sufficient.
answer choice B
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51% (02:07) correct 
