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

Answer 1

150

Explanation:

Using 8 rows leaves 2 positions unoccupied implies that the population of the number of members in the band is 2 less than a multiple of 8. That makes this an even number.

Similarly, we understand that the number of members is 3 less than a multiple of 9. So, If we list the even numbers that are 3 less than multiples of 9 between 100 and 200 and are even; we have:

117 – 3, 135 – 3, 153 – 3, 171 – 3, 189 – 3

= 114, 132, 150, 168, 186

Also, the numbers that are two less than a multiple of 8:

102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198

From above, we will realize that the number common in both is 150

Let's check if that satisfy our calculation;

SO:

150/8 = 18 remainder 6 ; Thus 8 - 6 = 2 (positions)

150/9 = 16 reminder 6 ; Thus 9 - 6 = 3 (positions)

Hence the number of members in the band if the membership is between 100 and 200 is 150