Question

A number when divided by 296 leaves 75 as remainder. When the same is divided by 37, the remainder will be:
A. 1
B. 2
C. 8
D. 11

Answer 1

Hint: In the above type of question we will assume the dividend to be a variable and we will write the dividend in the form of their quotient and remainder and rearrange them to get the answer.

Complete step-by-step answer:

Let the number be x, q be the quotient when divided by 296, leaves 75 as remainder.
$\Rightarrow x=296q+75$

Now when we will divide the same number by 37 it can be written as,
\[\dfrac{x}{37}=\dfrac{296q}{37}+\dfrac{75}{37}\]

Here, 296 is completely divisible by 37 by 8 times so whatever comes out the remainder on dividing 75 by 37 will be the final answer.
\[75\div 37\] gives 1 as remainder.

Hence, the remainder when the number is divided by 37 is equal to 1.
Therefore, the correct option of the above question is option A.

Note: Just remember the terms related to division like quotient, remainder, dividend and divisor as it will help you in these types of questions. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient and the number left over is called the remainder.