If a is a positive integer, and if the units digit of a^2 is 1 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?
Choose the correct choice from the following choices:
A) 1
B) 3
C) 5
D) 7
E) 9
If the units digit of a^2 is 1, then the units digit of a is either 1 or 9.   If the units digit of (a+1)^2 is 4, then the units digit of a+1 is either 2 or 8.   To satisfy both conditions, the units digit of a must be 1.   Then a+2 has the units digit of 3, thus the units digit of (a+2)^2 will be 9.   The answer is 9.
<result>E</result>
If a is a positive integer, and if the units digit of a^2 is 1 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?