SOLUTION: A list of numbers 2, 4, 8, . . . is formed by doubling each of the preceding numbers. What is the remainder when the 15th number is divided by 6?
(A) 0 (B) 2 (C) 4 (D) 6 (E) 8
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Question 367082: A list of numbers 2, 4, 8, . . . is formed by doubling each of the preceding numbers. What is the remainder when the 15th number is divided by 6?
(A) 0 (B) 2 (C) 4 (D) 6 (E) 8
Answer by Jk22(389) (Show Source): You can put this solution on YOUR website!
The number is 2^15
the remainder of division by 6 can be 0,1,2,3,4,5, 0 is impossible since it's not divisible by 6
1+6n is odd, hence cannot be 1 (except for 2^0=1)
2+6n 2, is possible
3 and 5 impossible since odd.
Hence the possible remainder are 2 or 4.
Induction : let n>0
Suppose 2^n has a remainder 2 divided by 6 : 2^n = 2 + 6n
then 2^(n+1)= 4 + 12n = 4 + 6*2n, the remainder were 4.
Hence the remainder are alternating 2,4,2,
if the exponent is odd, the remainder is 2, else 4
hence for 15, the remainder is 2, answer (B)
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