Multiple choice

A number N, when divided by 23, leaves a remainder 19. What will be the remainder when (2N + 1) is divided by 23?

  1. 15

  2. 16

  3. 19

  4. 20

  5. 39
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B Correct answer
Explanation

Given N = 23k + 19. We need the remainder of (2N + 1) / 23. Substituting N, we get 2(23k + 19) + 1 = 46k + 38 + 1 = 46k + 39. Dividing 39 by 23, the remainder is 39 - 23 = 16.

AI explanation

By the Euclidean division theorem, N can be written as 23k + 19. Substituting this into the expression gives 2N + 1 = 2(23k + 19) + 1 = 46k + 38 + 1 = 46k + 39. When 46k + 39 is divided by 23, the 46k part divides perfectly and the remainder is the remainder of 39 divided by 23, which is 16. The result is 16.

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