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When a number is divided by 3 it leaves remainder as $5 .$ What will be the remainder when $3 \mathrm{n}+3$ are divided by 3 ?
a) 0
b) 3
c) 9
d) 6
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a

Explanation:

Let the number be $\mathrm{n}$. If the number is divided by 3 it leaves 5 as remainder. By Euclid's division lemma, $\mathrm{n}=3 \mathrm{q}+5$ where $\mathrm{q}$ is quotient $3 n=3(3 q+5)$
$3 n=9 q+15$
$3 n+3=9 q+18=3 \times 3 q+3 \times 6=3(3 q+6)$
Hence, the remainder is $0 .$

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