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., 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

---

More Questions Answers on Number Theory

CAT, XAT, TANCET Practice Questions and Answers : Listed Topicwise

Number Theory		Permutation Combination		Probability		Inequalities
Geometry		Mensuration		Trigonometry		Coordinate Geometry
Percentages		Profit Loss		Ratio Proportion		Mixtures Alligation
Speed Time Distance		Pipes Cisterns		Interest		Races
Average, Mean		AP, GP, HP		Set Theory		Clocks Calendars
Algebra		Function		English Grammar		General Awareness
Data sufficiency		TANCET Papers		XAT Papers