Question

Seven integers, x1, x2, x3, x4, x5, x6, and x7, are picked at random from the set of all integers between 10 and 110, inclusive. If each of these integers is divided by 7 and the 7 remainders are all added together, what would be the sum of the 7 remainders?

Answer 1

0+1+2+3+4+5+6=21

Explanation:

Since integers are given as x1, x2, x3, x4, x5, x6, and x7. This means they are consecutive integers divisible by 7.

Thus no matter which 7 consecutive integers are these, their reminders will always be in the order of 0,1,2,3,4,5 & 6.

So their sum will be 0+1+2+3+4+5+6=21.