XY13-3-32

Radia_ting

Seven different numbers are selected from the integers 1 to 100, and each number is divided by7.

What is the sum of remainders?

(1) The range of the seven remainders is 6

(2) The seven numbers selected are consecutive integers.

answer B. Needs explaination, please.

sweetcorns

因为能被7整除的数是每7个数出现一次，所以7个连续整数比如1234567或者 11，12，13，14，15，16，17被7除后的余数是固定的123456，条件2满足；条件1不充分，比如，1，6，11，22，36，43，50，因为需要range，只要满足其中一个比7的倍数小1，另一个大1就够了，其余另取则余数不固定，自然sum也不固定.

Radia_ting

Thank you so much .