Number systems  Quant/Math  CAT 2016
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 d_{1} and d_{2} and two remainders r_{1} and r_{2} are obtained, the remainder that will be obtained by the product of d_{1} and d_{2} is given by the relation
d_{1}r_{2} + r_{1}.
Where d_{1} and d_{2} are in ascending order respectively and r_{1} and r_{2} are their respective remainders when they divide the number.
In this case, the d_{1} = 8 and d_{2} = 11. And r_{1} = 3 and r_{2} = 7
Therefore, d_{1}r_{2} + r_{1} = 8*7 + 3 = 59.
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