SOLUTION: When n is divided by 4, the remainder is 3. What is the remainder when (3n-1)) is divided by 4? A)0 B)1 C)2 D)4

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Question 1144973: When n is divided by 4, the remainder is 3. What is the remainder when (3n-1)) is divided by 4?
A)0
B)1
C)2
D)4
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
n = 4x +3, where x is an integer
:
(3(4x +3))/4 = ((12x +9) - 1)/4 = (12x +8)/4 = 3x +2
:
remainder is 2
:
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answer is C) 2
*********************
:

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
When n is divided by 4, the remainder is 3 (given).


Hence, when 3n is divided by 4, the remainder is 3*3 = 9, which is EQUIVALENT to the remainder 1 modulus 4.


It implies, that when (3n-1) is divided by 4, the remainder is 0.     ANSWER



Example.  Let n = 7,    giving the remainder 3 when divided by 4.

          3n = 21,      giving the remainder 1 when divided by 4.

          (3n-1) = 20,  giving the remainder 0 when divided by 4.