If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 6, what is the units digit of (a+2)^2?
Choose one
A) 1
B) 3
C) 5
D) 6
E) 8
If the units digit of a^2 is 9, then the units digit of a is either 3 or 7.   If the units digit of (a+1)^2 is 6, then the units digit of a+1 is either 4 or 6.   To satisfy both conditions, the units digit of a must be 3.   Then a+2 has the units digit of 5, thus the units digit of (a+2)^2 will be 5.   The answer is 5.
<result>C</result>
If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 6, what is the units digit of (a+2)^2?