Question 4 the day : June 21, 2002

The question for the day is from the topic of Number systems. It is a question about Successive Division.

It is important that you know some of the theorems related to number systems. For instance, how the remainders and divisors behave and the relationship between them.

Here is a problem which uses the relationship between remainders and divisors.

Question
A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?

(1) 3
(2) 21
(3) 59
(4) 68

Correct Choice is (3) and Correct Answer is 59

Explanatory Answer

When a number is successfully divided by two divisors d₁ and d₂ and two remainders r₁ and r₂ are obtained, the remainder that will be obtained by the product of d₁ and d₂ is given by the relation

d₁r₂ + r₁.

Where d₁ and d₂ are in ascending order respectively and r₁ and r₂ are their respective remainders when they divide the number.

In this case, the d₁ = 8 and d₂ = 11. And r₁ = 3 and r₂ = 7
Therefore, d₁r₂ + r₁ = 8*7 + 3 = 59.

1. Factors, divisors; Prime Factors		2. Test of divisibility by 3, 4, 5 and 7
3. Framing equation : Word Problem		4. Operations on odd and even numbers
5. Remainders of division by a factor of 'd'		6. Sum of first 'n' natural numbers : AP
7. Number of factors of a positive integer		8. Is 1025 - 7 divisible by 3?
9. How to find the HCF / GCD of numbers?		10. Test of Divisibility by 8 and 11.
11. Number Properties : Products		12. Numbers, Fractions - TANCET '08
13. LCM, Number theory - XAT 2012		14. Number of divisors / factors
15. Highest power dividing a factorial		16. Right Triangles - Squares of numbers
17. Comparing Numbers : TANCET 2008

Sorted by Subject
Algebra, Arithmetic & Geometric Progressions, Averages and Mean, Clocks and Calendars, Data Sufficiency, English Grammar, Function, Geometry, Coordinate Geometry, Mensuration, Trigonometry, Interest, Inequality, Mixtures & Alligations, Number System and Theory, Percentages, Profit & Loss, Permutation & Combination, Probability, Ratio, Proportion, Set Language and Theory, Speed, Time & Distance, Races, Pipes & Cisterns And Work & Time, Miscellaneous, General Knowledge.