Multiple choice

When a number divided by 114 it leaves a remainder 14. What will be the remainder, when the same number divided by 19.

  1. 12

  2. 14

  3. 10

  4. 16
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B Correct answer
Explanation

Let N = 114k + 14. We want N mod 19. 114 = 19 * 6, so 114k is divisible by 19. N mod 19 = 14 mod 19 = 14.

AI explanation

Let the number be 114q plus 14, where q is the quotient. Since 114 is a perfect multiple of 19, the term 114q is completely divisible by 19. Thus, the remainder depends only on the number 14 divided by 19, which leaves a remainder of 14. The result is 14.

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