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Question
A positive integer m when divided by 11 gives remainder 6. If 4m + 5 is divided by 11, the remainder is ______.
Fill in the Blanks
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Solution
A positive integer m when divided by 11 gives remainder 6. If 4m + 5 is divided by 11, the remainder is 7.
Explanation:
Let m = 11k + 6 for some integer k.
Then 4m + 5 = 4(11k + 6) + 5
= 44k + 24 + 5
= 44k + 29
= 11(4k + 2) + 7
So the remainder is 7.
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