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Standard X

Mathematics

Division Algorithm for a Polynomial

When a natura...

Question

When a natural number $n$ is divided by $4$ , the remainder is $3$ . What is the remainder when $2 n$ is divided by $4$ ?

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Solution

The correct option is B $2$
$n = 4 q + 3 \Rightarrow 2 n = 8 q + 6$
$\Rightarrow 2 n = (8 q + 4) + 2 = 4 (2 q + 1) + 2$
$∴ R e m a i n d e r i s 2$

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When a natural number n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4?

The correct option is B 2n=4q+3⇒2n=8q+6⇒2n=(8q+4)+2=4(2q+1)+2∴Remainderis2

When a natural number $n$ is divided by $4$ , the remainder is $3$ . What is the remainder when $2 n$ is divided by $4$ ?

The correct option is B $2$
$n = 4 q + 3 \Rightarrow 2 n = 8 q + 6$
$\Rightarrow 2 n = (8 q + 4) + 2 = 4 (2 q + 1) + 2$
$∴ R e m a i n d e r i s 2$