Multiple choice

A number divided by 119 gives 19 as the remainder. What is the remainder when the same number is divided by 17?

  1. 0

  2. 2

  3. 5

  4. 7

  5. 9
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B Correct answer
Explanation

Let the number be N = 119k + 19. We want the remainder when N is divided by 17. Since 119 = 17 * 7, 119k is divisible by 17. The remainder is the same as 19 divided by 17, which is 2.

AI explanation

Let the unknown number be N, so we can write N = 119q + 19, where q is the quotient. Because 119 is perfectly divisible by 17, we can rewrite the expression as N = 17(7q) + 17 + 2, which simplifies to 17(7q + 1) + 2. This shows that when N is divided by 17, the remainder is 2.

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