Question

A number when divided by d leaves a remainder of 8 and when divided by 3d leaves a remainder of 21. What is the remainder left, when twice the number is divided by 3d?

Answer 1

Answer:

3

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Step-by-step explanation:

Let n be the number

n divided by d leaves remainder 8

=> n = da + 8, for some a

n divided by 3d leaves remainder 21

=> n = 3db + 21, for some b

So

da + 8 = 3db + 21  =>  d ( a - 3b ) = 21 - 8 = 13

Since 13 is prime, this means that d = 13  ( supposing that d has to be positive ).

So

n = 3db + 21 = 39b + 21

=> 2n = 39(2b) + 42 = 39(2b) + 39 + 3 = 39 ( 2b + 1 ) + 3

=> 2n divided by 39 leaves remainder 3