Question

When a number \[P\] is divided by \[4\] it leaves the remainder \[3\] . If twice of the number \[P\] is divided by the same divisor \[4\], then will there be the remainder?
\[\begin{align}
  & A.0 \\
 & B.1 \\
 & C.2 \\
 & D.6 \\
\end{align}\]

Answer 1

Hint: In order to find the remainder of twice of a number given, when divided by the same divisor, firstly, we have to express the given statement in mathematical form as per the division rule. Then we have to check for the same for twice the number to evaluate the remainder but the remainder should be in simplest form which means it should not be further divisible.

Complete step by step answer:
Now let us learn about linear equations. A linear equation can be expressed in the form any number of variables as required. As the number of the variables increase, the name of the equation simply denotes it. The general equation of a linear equation in a single variable is \[ax+b=0\]. We can find the linear equation in three major ways. They are: point-slope form, standard form and slope-intercept form.
Now let us find the remainder, if twice the number \[P\] is divided by the same divisor \[4\].
Firstly, let us find the remainder for the original number.
We get,
\[P=4x+3\]
The remainder of the original number is \[3\] as mentioned.
Now let us find the remainder of the twice of the number.
\[2P=2\left( 4x+3 \right)\]
We can see that if the number is doubled, the remainder and the quotient will also get doubled.
Upon simplifying, we obtain the remainder as
\[2P=8x+6\]
We get the remainder as \[6\]when the given number is doubled.
But we can see that \[6\] is not in the simplest form, we can write it as \[4+2\]
So we can conclude that \[2\] would be the remainder when the twice of a number is divided by \[4\].

So, the correct answer is “Option C”.

Note: We must have a note that the remainder we obtain must be in the simplest form. We can solve it by considering a random number such that when divided by \[4\], we get \[3\] as the remainder.
So the number we are going to consider would be \[7\].
Because, \[7=4(1)+3\]
So now twice of \[7\] is \[14\].
Now let us find the remainder of \[14\], when divided by the same divisor \[4\].
We obtain,
\[14=4(3)+2\]
We can see that the remainder we obtain is \[2\].
Hence, we can follow any of the methods, but when the divisors are larger, then it would be easier if we opt the method of solving by linear equations.