swerve wrote: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 4, what is the units digit of (a+2)^2?
A. 1
B. 3
C. 5
D. 6
C. 14
Let a=7, with the result that a² = 7² = 49 and that (a+1)² = (7+1)² = 8² = 64.
In this case:
(a+2)² = (7+2)² = 9² = 81.
Thus, the units digit of (a+2)² is 1.
The correct answer is
A.
Can I say that a=3?
If a=3, then (a+1)² = (3+1)² = 4² = 16, which violates the condition that (a+1)² has a units digit of 4.
Thus, it is not possible that a=3.
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