If K is a positive integer, what is the remainder when (13^4K+2) +8 is divided by 10?
A) 7
B) 4
C) 2
D) 1
E) 0
Answer:[spoiler] (A) 7 [/spoiler]
Official explanation requires one to calculate 13^4 = 28561, then multiply by 13^2 = 169, to conclude that the units digit must be 9, and thus when 8 is added the final units digit becomes 7, yielding a remainder of 7 when divided by 10. Is there a better way to do this problem?
A) 7
B) 4
C) 2
D) 1
E) 0
Answer:[spoiler] (A) 7 [/spoiler]
Official explanation requires one to calculate 13^4 = 28561, then multiply by 13^2 = 169, to conclude that the units digit must be 9, and thus when 8 is added the final units digit becomes 7, yielding a remainder of 7 when divided by 10. Is there a better way to do this problem?
