SOLUTION: A number N when divided by 5 leaves remainder 1 and when divided by 6 leaves remainder 3. Find the remainder when N is divided by 30. a) 19 b) 17 c) 15 d) 21

Question 1038890: A number N when divided by 5 leaves remainder 1 and when divided by 6 leaves remainder 3. Find the remainder when N is divided by 30.
a) 19 b) 17 c) 15 d) 21

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
N is congruent to 1 modulo 5
N is congruent to 3 modulo 6
:
N - 1 is divisible by 5
N - 3 is divisible by 6
:
we can use the answers as remainders which are congruent to N
:
a) 19
19 -1 = 18 is not divisible by 5
b) 17
17 -1 = 16 is not divisible by 5
c) 15
15 -1 = 14 is not divisible by 5
d) 21
21 - 1 = 20 is divisible by 5
21 - 3 = 18 is divisible by 6
********************************
the answer is d, 21 since
21 is congruent to 21 modulo 30
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