Answer: 210
Explanation:
Let's say that n is the number we are looking for. So ...
n / 5 = an integer
n / 3 = an integer
n / 4 does not equal an integer.
n = even
n = a triangular number
n / 9 does not equal an integer
First let's look at what even numbers there are that are multiples of 5 and 3:
30,60,90,120,150,180,210,240,270,300, etc...
Now let's eliminate those that are divisible by 4 and create a new list:
30,90,150,210,270
Next, let's eliminate those that are divisible by 9 and create a new list:
30,150,210
Finally, let's eliminate the non-triangular numbers and find the value of n:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210...
As you can see, 210 is the only number out of those that were remaining which appears in the list of triangular numbers, so n = 210.