Question 1143922: When K is divided by 4, the remainder is 1. What is the remainder when (3k-1) is divided by 4?
A)0
B)1
C)2
F)4
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! k / 4 = x + 1/4, where x is an integer and the remainder is 1.
solve for k to get k = 4x + 1
when x = 0, k = 1
when x = 1, k = 5
when x = 2, k = 9
when k = 1, you get 1/4 = 0 + 1/4
when k = 5, you get 5/4 = 1 + 1/4
when k = 9, you get 9/4 = 2 + 1/4
the value of k can be 1, 5, 9, 13, 17, ....
we'll assume k = 17
k/4 = 17/4 = 4 + 1/4
the remainder is always 1.
when k 17, (3k-1)/4 becomes 50/4 = 12 + 2/4
when k = 9, (3k-1)/4 becomes 26/4 = 6 + 2/4
when k = 5, (3k-1)/4 becomes 14/4 = = 3 + 2/4
the remainder is always 2.
that's your solution.
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
K divided by 4 leaves remainder 1 --> k = 1, mod 4.
Then by the simple rules of modular arithmetic,
3k = 3*1 = 3, mod 4
3k-1 = 3-2 = 2, mod 4
So 3k-1 leaves remainder 2 when divided by 4.
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