Problem Solving

The integer \(P\) is greater than \(7.\) If the integer \(P\) leaves a remainder of \(4\) when divided by \(9,\) all of the following must be true EXCEPT

A. The number that is \(4\) less than \(P\) is a multiple of \(9\)
B. The number that is \(5\) more than \(P\) is a multiple of \(9\)
C. The number that is \(2\) more than P is a multiple of \(3\)
D. When divided by \(3,\,P\) will leave a remainder of \(1\)
E. When divided by \(2,\,P\) will leave a remainder of \(1\)

The OA is E