Question : When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
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Correct Answer: 1
Solution :
Use: Dividend = Quotient × Divisor + Remainder
If $\mathrm{m}$ divided by 7 gives a remainder of 5, we can express $\mathrm{m}$ as $\mathrm{m} = 7\mathrm{k} + 5$ for some integer $\mathrm{k}$.
Substituting this into $3m$
$3\mathrm{m} = 3(7\mathrm{k} + 5) = 21\mathrm{k} + 15=7(3\mathrm{k}+2)+1$.
So, when $3\mathrm{m}$ is divided by 7, the remainder is 1.
Hence, the correct answer is 1.
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