Question

When a number is divided by 36, the remainder is 19. What will be the remainder when the number is divided by 12?
A. 7
B. 5
C. 3
D. 0

Answer 1

Hint: We will use the formula of division where we equate the value of the dividend with the sum of remainder with product of quotient and the divisor. We can also write the equation of any division as
Dividend \[ = \] Divisor \[ \times \] Quotient \[ + \] Remainder
For example, in the below division:
\[\begin{gathered}
  12\mathop{\left){\vphantom{1{72}}}\right.
\!\!\!\!\overline{\,\,\,\vphantom 1{{72}}}}
\limits^{\displaystyle \,\,\, 6} \\
  \underline { - 72} \\
   = 0 \\
\end{gathered} \]
The dividend is equal to 72, Divisor is equal to 12, Quotient is equal to 6 and Remainder is equal to 0.

Complete step-by-step solution:
Suppose we have to find the number \[n\]. So, as per the given information in the question when we divided the number\[n\] by divisor 36, it gives as a Quotient \[d\] remainder \[r = 19\].
So, by using the formula: Dividend \[ = \]Divisor \[ \times \]Quotient \[ + \]Remainder, we can write the equation as:
\[ \Rightarrow n{\text{ = 36}}d + 19\] … (1)
By breaking the term \[{\text{36 = 12}} \times 3\] and replacing it in the above equation (1), we get:
\[ \Rightarrow n{\text{ = 12}} \times {\text{3}}d + 19\]
By breaking the term \[{\text{19 = 12 + 7}}\] and replacing it in the above equation, we get:
\[ \Rightarrow n{\text{ = 12}} \times {\text{3}}d + 12 + 7\]
By taking 12 as a common from the LHS side of the above equation, we get:
\[ \Rightarrow n{\text{ = 12}}\left( {{\text{3}}d + 1} \right) + 7\]
Suppose \[3d + 1 = k\], replacing it in the above equation, we get:
\[ \Rightarrow n{\text{ = 12k}} + 7\]
So, by comparing the equation \[n{\text{ = 12k}} + 7\] with Dividend \[ = \]Divisor \[ \times \]Quotient \[ + \]Remainder , we get:
\[ \Rightarrow \]Dividend \[ = n\], divisor \[ = 12\], quotient \[ = k\] and remainder \[ = 7\]
So, we can say that when we divide the number by 12 it gives us a remainder 7.
\[\therefore \] Option A is correct.

Note: Many students make mistake of writing the remainder as 19 which also a possible case but since 19 is greater than 12 so it can be reduced on division to a number less than 12, so keep in mind the remainder is always less than the divisor and if it is greater than the divisor that means the division is incomplete.
Students need to remember the following terms, Dividend, Divisor, Quotient and Remainder, and relations between them. This plays an important role in solving these types of questions. Definitions of these following terms are as given below:
Dividend- The number that is divided is called a dividend.
Divisor- The number by which the dividend is being divided is known as the divisor.
Quotient- Quotient is the quantity produced by the division of two numbers.
The remainder- Remainder is known as the integer left over after dividing the dividend by divisor.