Remainders of division by a factor of 'd' : Number System
The question is a Number properties question. The question is about finding the remainder of the division of a number by a factor of a divisor 'd'; the remainder when a number is divided by the divisor 'd' is given.
Question
When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
- 10
- 7
- 19
- 192
- None of these
Correct Answer -
7. Choice (2)
Explanatory Answer
Let the number be 'a'.
When 'a' is divided by 36, let the quotient be 'q' and we know the remainder is 19.
i.e.,
![q/36 = q](images/remainders_divisibility_factors_040803_1.jpg)
and remainder is 19
or a = 36q + 19
when 'a' is divided by 12, we get
![36q + 19/12](images/remainders_divisibility_factors_040803_2.jpg)
or
![36q/12 + 19/12](images/remainders_divisibility_factors_040803_3.jpg)
.
36q is divisible by 12.
Therefore, remainder = 7
Correct answer choice (2)
Level of difficulty : Moderate
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