Question 103

A certain number when divided by 899 leaves the remainder 65. When the same number is divided by 31, the remainder is :

Solution

if the number N is divided by 899 and leaves a remainder 65 then N = 899K + 65

and hence when N will be divided by 31

remainder of $$\frac{899K + 65}{31}$$ = Remainder of $$\frac{65}{31}$$ as 899 is completely divisible by 31

and hence remainder is 3

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