jmc

Question

The members of a band are arranged in a rectangular formation. When they are arranged in 8 rows, there are 2 positions unoccupied in the formation. When they are arranged in 9 rows, there are 3 positions unoccupied. How many members are in the band if the membership is between 100 and 200?

Accepted Answer

The number of members in the band leaves a remainder of 6 when divided by 8 and a remainder of 6 when divided by 9. Therefore, the number of members is 6 more than a multiple of 98=72. The only such number between 100 and 200 is 72 2 + 6=150, so there are 150 members.