### Number systems - Remainders, divisors - questionbank - Ascent Education - XAT 2016, TANCET 2018 study material, correspondence course

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# 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?
1. 10
2. 7
3. 19
4. 192
5. None of these
Correct Answer - 7. Choice (2)

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., and remainder is 19

or a = 36q + 19

when 'a' is divided by 12, we get or .

36q is divisible by 12.

Therefore, remainder = 7

Correct answer choice (2)

Level of difficulty : Moderate

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