Question

If $122=q\times 6+r$, then the possible values of $r$ are:
A. 1, 2, 3, 4
B. 0, 1, 2, 3, 4, 5
C. 0, 1, 2, 3
D. 2, 3, 5

Answer 1

Hint: To solve this question, we are asked to find the range of $r$. So, for this, first of all we can use the remainder theorem. That is, in an equation $a=q\times n+r$, ‘$a$’ is dividend, ‘$q$’ is quotient, ‘$n$’ is the divisor and ‘$r$’ is the remainder. So, by using this theorem we can find the possible values of $r$.

Complete step by step answer:
As we are asked to find the possible values of $r$, we can use the remainder theorem. The remainder theorem can be explained with an equation $a=q\times n+r$ as ‘$a$’ is dividend, ‘$q$’ is quotient, ‘$n$’ is the divisor and ‘$r$’ is the remainder. Here, the $r$ should always lie in range $0\le r\le n$.
So, the equation $122=q\times 6+r$, the $r$ lies in the range of $0\le r\le 6$.
Therefore, the possible values of $r$ is 0, 1, 2, 3, 4, 5 and 6.

So, the option that is more accurate to the answer is option B. That is, the possible value of $r$ is 0, 1, 2, 3, 4, 5.

Note: Here, we have used the remainder theorem. That is, for an equation $a=q\times n+r$ as ‘$a$’ is dividend, ‘$q$’ is quotient, ‘$n$’ is the divisor and ‘$r$’ is the remainder. Here, we have to keep in mind that the remainder should always lie in the range of $0\le r\le n$ so we can reach the answer directly by eliminating the option. Otherwise, we can simply substitute the values and check if the values are possible or not.