Multiple choice

When the positive integer $m$ is divided by $5$, the remainder is $3$. What is the remainder when $20m$ is divided by $25$?

  1. 10

  2. 15

  3. 20

  4. 25
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A Correct answer
Explanation

m = 5k + 3. Then 20m = 20(5k + 3) = 100k + 60. Dividing 100k + 60 by 25: 100k is divisible by 25, and 60 divided by 25 leaves a remainder of 10.

AI explanation

Since the positive integer m leaves a remainder of 3 when divided by 5, write it as m = 5k + 3. Multiply this by 20 to get 20m = 20(5k + 3) = 100k + 60. Divide 100k + 60 by 25 to find the remainder. The term 100k is divisible by 25, and 60 divided by 25 leaves a remainder of 10.

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