SOLUTION: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7?

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Question 1192367: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7?
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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The problem says

    x  = 7n + 5  for some integer n.


Multiply it by 5

    5x = 5*(7n) + 5*5 = 35x + 25 = 7*(5n) + 25.


It means that 5x, when divided by 7, gives the same remainder, as the number 25.


Thus the sough remainder is  25 mod 7 = 4.    ANSWER

Solved.