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You are here: Home CAT Math Number Theory Remainders of Successive division

Number systems - Quant/Math - CAT 2012

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.


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