Question

When N is divided by 4, the remainder is 3. What is the remainder when 2N is divided by 4?

Answer 1

Hint:To find the remainder of the value 2N divided by 4 is given as \[n=4q+r\] where n is the dividend, q is the quotient and r is the divisor, first we use the value to find the equation of N divided by 4 with remainder 3 and then replace N by 2N and find the value of the remainder.

Complete solution step by step:
First let us form the equation for the first case where N is divided by 4 leaving a remainder of 3 as given below:
\[\Rightarrow n=4q+r\]
Placing the values in the above formula, we get the equation between dividend, quotient and remainder as:
\[\Rightarrow N=4q+3\]
Now that we have got the value of N, so we can find the value of \[2N\] as well where we double the value of N as:
\[\Rightarrow 2N=2\left( 4q+3 \right)\]
And placing the above value of N in the formula \[n=4q+r\], we get the equation as:
\[\Rightarrow 2N=8q+6\]
Now the value [\8q+6\] if divided by 4 will give the remainder as:
\[\Rightarrow \dfrac{8q}{4}+\dfrac{6}{4}=2q+\dfrac{3}{2}\]
As we can see in the above part the divisor \[4\] divides the value of \[6\] but could not divide it completely leaving a remainder of \[2\].
Therefore, the remainder when dividing \[2N\] by \[4\], we get the value of the remainder as \2\.

Note: Another method to solve the question is by assuming a value for N which gives a remainder \[3\], the most closest value one can assume is \[12\] where if \[12\] is divided by \[4\], we get the remainder as \[3\]. Now if we double the value of \[15\] we get \[30\] and if we divide the value of \[30\] by \[28\] which is a multiple of \[4\] leaving us with a remainder of \[2\].