Multiple choice

A number when divided by $143$ leaves $31$ as remainder. What will be the remainder when the same number is divided by $13$?

  1. $0$
  2. $1$
  3. $3$
  4. $5$
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D Correct answer
Explanation

If a number N = 143k + 31, then N = (11 * 13)k + (2 * 13 + 5). N = 13 * (11k + 2) + 5. The remainder when divided by 13 is 5.

AI explanation

Let the number be represented as 143k + 31, where k is an integer. Because 143 is perfectly divisible by 13, dividing 143k by 13 leaves a remainder of 0. Divide the remainder 31 by 13 to get the final remainder. 31 divided by 13 gives a quotient of 2 and a remainder of 5.

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