Question 123

A number when successively divided by 5 and 6 gives remainders 3 and 2 respectively. What will be the remainders if the number is successively divided by 3 and 4 ?

Solution

Going in the reverse order

When a number is divided by 6, the remainder is 2 => the number is of the form 6k+2

When 6k+2 is divided by 5,the remainder is 3 => the number is of the form 5(6k+2)+3 = 30k+13

When 30k+13 is divided by 3, the remainder is 1.

The remaining is 3(10k+4), so when 10k+4 is divided by 4, the remainder is 0 or 2

Among the given options 1, 2 satisfies this condition.

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