Question

If \[n\] is a whole number which when divided by \[4\] gives \[3\] as remainder. What will be the remainder when \[2n\] is divided by \[4\] ?
A. \[7\]
B. \[5\]
C. \[4\]
D. \[2\]

Answer 1

Hint: We are given with a condition that if a whole number \[n\] is divided by \[4\] gives \[3\] as remainder. And we are asked the remainder when \[2n\] is divided by \[4\] . For this recall the concepts of dividend, quotient and remainder and use those to find the required answer.

Complete step-by-step answer:
Given the whole number \[n\]
Quotient of the whole number is \[4\]
Remainder is \[3\]
We can write a whole number as,
 \[{\text{Dividend}} = ({\text{divisor}} \times {\text{quotient}}) + {\text{remainder}}\]
Here,
 \[{\text{Dividend}} = n\]
 \[{\text{quotient}} = 4\]
 \[{\text{remainder}} = 3\]
Let the divisor be \[q\]
Now, we can the whole number \[n\] as
 \[n = \left( {q \times 4} \right) + 3\]
 \[ \Rightarrow n = 4q + 3\] (i)
We are asked what will be the remainder when \[2n\] is divided by \[4\] , for this we multiply equation (i) by \[2\] .
And we get equation (i) as,
 \[2n = 2 \times \left( {4q + 3} \right)\]
 \[ \Rightarrow 2n = 8q + 6\]
 \[ \Rightarrow 2n = 8q + 4 + 6 - 4\]
 \[ \Rightarrow 2n = 4(2q + 1) + 2\] (ii)
Comparing equation (ii) with the general equation \[{\text{Dividend}} = ({\text{divisor}} \times {\text{quotient}}) + {\text{remainder}}\] we get, for the whole number \[2n\] if divided by \[4\] the divisor is \[(2q + 1)\] and remainder is \[2\] .
So, the correct answer is “Option D”.

Note: While proceeding for any questions first always evaluate the given conditions and relate those with the quantity you need to find out. Most of the time students get confused with where to start from, so always check for the other information given in the question and try to evaluate them and relate them to the quantity you are asked to find out. As in this question we were given the information for a whole number \[n\] and we were asked about \[2n\] so we can easily observe one number is twice the other one, similarly we need to check for other questions too.