Wednesday, September 29, 2010

If n[i] and m are positive integers, what is the remainder when

If n[i] and m are positive integers, what is the remainder when "3^(4n+2) + m" is divided by 10 ?

(1) n = 2
(2) m = 1











3^1 =3 ,3^2=9,3^3=27,3^4 =81,3^5 = 243
notice a pattern in the units digit? they repeat every fourth power. 3^1 & 3^5 have the same units digit,3^2 & 3 ^6 have the same units digit & so on
using (1)
9*3^4n + m becomes 9*3^8 + m
considering only units digit , 9*1 + m
INSUFFICENT
using (2)
9*3^4n + 1 , as shown above, for all values of n, units digit 3^4n remains the same. ( UD of 3^4=1,UD of 3^8 =1)
Now , considering only units digit
9*1 + 1 = 10 ,Hence B SUFFICIENT

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