Multiple choice

James is thinking of a number. If he divides it by 4 and 5 successively, the remainders are 3 and 4, respectively. What will be the remainder, if James divides the same number by 20?

  1. 9

  2. 13

  3. 17

  4. 19

  5. 21
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D Correct answer
Explanation

Let the number be N. N = 4a + 3. a = 5b + 4. N = 4(5b + 4) + 3 = 20b + 16 + 3 = 20b + 19. Dividing by 20 leaves a remainder of 19.

AI explanation

Let the number be N. When N is divided by 5, the remainder is 4, so we can write N = 5k + 4 for some integer k. When this quotient k is divided by 4, the remainder is 3, meaning k can be written as 4m + 3. Substituting this into the equation for N gives N = 5(4m + 3) + 4 = 20m + 15 + 4 = 20m + 19. This shows the number is of the form 20m + 19, so dividing it by 20 leaves a remainder of 19.

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