SOLUTION: When a number n is divided by 7, the remainder is 2. What is the remainder when 2n+1 is divided by 7?

SOLUTION: When a number n is divided by 7, the remainder is 2. What is the remainder when 2n+1 is divided by 7?

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Question 1049143: When a number n is divided by 7, the remainder is 2. What is the remainder when 2n+1 is divided by 7?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
When a number n is divided by 7, the remainder is 2

So n is 2 more than some multiple of 7, so

n = 7k+2, for some positive integer k.

What is the remainder when 2n+1 is divided by 7?

2n+1 = 2(7k+2)+1 = 14k+4+1 = 14k+5

When 14k+5 is divided by 7,

   2k+0
7)14k+5  
  14k
      5
      0
      5

So the remainder is 5.

Edwin

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