Question 47

A positive integer when divided by q leaves remainder 21. When double that number is divided by q, the remainder is 13. Then, q is _________.

Solution

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Let the positive no. be N

N = kq + 21

N' = 2N = 2kq + 42

Now N' leaves a remainder of 13 when divided by q

So, N' = pq + 13

Therefore Remainder when 42 is divided by q should be 13 which is only possible when q=29.

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