Discussion
A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?
Answer: C
Let the number be N. Let the quotient when divided by 3 be q. So, \(N = 3q+1\). We are given that when q is divided by 2, the remainder is 1. So, \(q = 2k+1\) for some integer k. Substitute this expression for q into the first equation: \(N = 3(2k+1)+1 = 6k+3+1 = 6k+4\). This shows that when the number N is divided by 6, the remainder is 4.
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