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You are here: Home   XAT, TANCET Prep Questions  Number Theory   Remainders, divisors Question 5

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)

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 and remainder is 19

or a = 36q + 19

when 'a' is divided by 12, we get 36q + 19/12 or 36q/12 + 19/12.

36q is divisible by 12.

Therefore, remainder = 7

Correct answer choice (2)

Level of difficulty : Moderate



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