When the positive integer $$m$$ is divided by $$7$$, the remainder is $$4$$. What is the remainder when $$2m$$ is divided by $$7$$ ?

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Uniteasy Admin · Accepted Answer

If $$ m$$ is divided by $$7$$, the remainder is $$4$$
$$m = 7q+4$$ (q is positive integer) 
Then
$$2m = 2(7q+4) = 14q+8 $$
When divided by 7,
$$\dfrac{2m}{7} = \dfrac{14q+8}{7} = 2q+1+\dfrac{1}{7}  $$
Therefore the remainder is $$1$$
For example, 11 is divided by 7, the remainder is 4. When 22 is divided by 7, the remainder is 1.
B is correct

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