Multiple choice

Let 'm' be an integer greater than 10. When 'm' is divided by 8, the remainder is 5. What is the remainder when (4m - 3) is divided by 16?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 5
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B Correct answer
Explanation

m = 8k + 5. Then 4m - 3 = 4(8k + 5) - 3 = 32k + 20 - 3 = 32k + 17. Dividing 32k + 17 by 16 gives a remainder of 1.

AI explanation

Using the division algorithm, if m divided by 8 leaves a remainder of 5, we can write m as 8k plus 5 for some integer k. Substituting this into the expression (4m minus 3) gives 4 times (8k plus 5) minus 3, which simplifies to 32k plus 17. When dividing 32k plus 17 by 16, the term 32k is perfectly divisible by 16, leaving a remainder from 17 divided by 16. Since 17 divided by 16 equals 1 with a remainder of 1, the final remainder is 1.

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