Ivan must choose a number between 49 and 95 that is a multiple or 3,5, and 9, write all the numbers that he could choose.

Question

if there is more than one number, seperate them with commas.

Answer 1

If it has to be multiple of all three of those numbers, there is only one solution between 49 and 95, which is 90.

Answer 2

Here's a nice trick for figuring out the numbers:

For multiples of 3, note that the sum of all terms in numbers which are multiples of 3 add to 3, 6, 9,12,15 etc. thus:

51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93.

For multiples of 5, the second term must be a 5 or 0, thus:

50, 55, 60, 65, 70, 75, 80, 85, 90, 95.

For multiples of 9, the terms must add to 9 or 18, thus:

54, 63, 72, 81, 90

 

In summary, the term repeated in all three is:

90

 

A shorter way of solving this would be to take the smallest number all three are factors of (9*5 = 45). Then you know that the solution must be a multiple of 45, which the only multiple of 45 within 49 and 95 is 90.