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A number when divided by $259$ leaves a remainder $139$. What will be the remainder when the same number is divided by $37$?
A. $28$
B. $29$
C. $30$
D. $31$

Last updated date: 13th Jun 2024
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Hint: The above statement can be converted into mathematical form using variables and equations. Any number and its divisor can be represented in the form:
             Number $ = $$($ Quotient $ \times $Divisor$)$$ + $ Remainder
We can use this result to use an approach for solving the question. Variables can be used to represent unknown constants like the quotient. So, by using simple calculations, the solution will be achieved.

Complete step-by-step answer:
It is given in the question that, when the number is divided by $259$ leaves the remainder $139$.
Since we do not know the exact value of the number, we can represent it by using a variable to use it in mathematical form. This will be a better approach to solve our question. Using Variables for unknown constants will simplify our approach.
Let the number be $x$.
So, when $x$ is divided by 259, it leaves a quotient too. Let it be $A$.
Now, it can be mathematically expressed as,
$x = \left( {A \times 139} \right) + 139$
Now in the next(new) case, $x$ is divided by $37$
It can be written as,
$\dfrac{x}{{37}} = \left( {A \times \dfrac{{259}}{{37}}} \right) + \dfrac{{139}}{{37}}$
Since $259$ is divisible by $37$,
$\dfrac{x}{{37}} = $$A \times 7 + \dfrac{{139}}{{37}}$
We can replace the product of two constants by another constant so that the equation might not look complex.
$\dfrac{x}{{37}}$ = $A' + \dfrac{{139}}{{37}}$
On dividing $139$ by $37$, we get remainder as 28. This can be written in the same quotient remainder format. So,
$\dfrac{x}{{37}}$ = $A' + 3 + \dfrac{{28}}{{37}}$
Again, we can replace the sum of two constants as one constant. It is done to simplify the equation and avoid any confusion.
$\dfrac{x}{{37}}$ = \[A'' + \dfrac{{28}}{{37}}\]
Now we will eliminate the denominator by multiplying both sides with $37$ .
$x$ = $A'' \times 37 + 28$
Therefore on dividing the number by $37$, the remainder will be $28$.

So, the correct answer is “Option A”.

Note: This problem can also be easily solved by directly dividing the term $A \times 259 + 139$ and getting the remainder as our solution. The Student must not be confused during the calculations. To avoid any error, the statement of the question must be read word by word while converting it into mathematical form. Further, remember that we can use variables wherever necessary, but they should be eliminated somehow till we reach our pure solution.