Question

the digits of a positive integer n are four consecutive integers in decreasing order when read from left to right. what is the sum of the possible remainders when n is divided by 37? [217]

Answer 1

Keeping in view that; the digits of a positive integer n are four consecutive integers in decreasing order when read from left to right.

The possible number can be ;

9876, 8765, 7654, 6543, 5432, 4321, 3210.

Dividing each by 37, you will get the remainders as 34, 33, 32, 31, 30, 29, 28

Hence, the sum of possible remainders is 217.