Question

Write one digit on each side of 15 to make a four digit multiple of 15. How many different solutions does this problem have? The possible solutions are.....

Answer 1

1155, 3150, 4155, 6150, 7155, 9150

There are 6.

Explanation:

First, the number would have to end in 0 or 5.

So if we try 1150 it does not divide but 1155 is a multiple.

Also the number would also be divisible by 3 so the sum of its digits would also have to be divisible by 3 so this rules out 2 being the first digit .

3150 is a multiple but not 3155

4155 is a multiple.

5xxx cannot be , 6150 is , so is 7155 ,

8xxx cannot be . 9150 is.

Answer 2

There are 6 solutions

Explanation:

All multiples of 15 are multiples of 5, then all finish in 0 or 5. Therefore, the four digits possibilities are: 1150 , 1155 , 2150 , 2155 , 3150 , 3155 , 4150 , 4155 , 5150 , 5155 , 6150 , 6155 , 7150 , 7155 , 8150 , 8155 , 9150 and 9155 . Only 1155 , 3150 , 4155 , 6150 , 7155 and 9150 are multiples of 15.