What is a number between 400 and 500 that is divisible by 3 but not 2?

Answer 1

I have provided the answers at the end, however if you are interested and learning the mathematical way to solve this, I have also provided the method I find easiest.

Not divisible by 2 is just another way of saying an odd number.

To find a number that is divisible by 3, you can use a neat trick, called digital roots. What this means, is to just sum up all the digits until you have a single digit.

Example: Find the digital root of 994

9 + 9 + 4 = 22 <--- this is not a single digit, repeat the process

2 + 2 = 4, the digital root of 994 is 4

Now, when a digital root is equal to 3, 6, or 9 that means the number is divisible by 3.

So we need some number between 400 and 500, whose digital root is equal to 3, 6, or 9 and is an odd number.

This helps find the first number that meets the condition, which is:

4 + 0 + 0 = 4

4 + 0 + 1 = 5

4 + 0 + 2 = 6, but 402 is even

4 + 0 + 3 = 7

4 + 0 + 4 = 8

4 + 0 + 5 = 9 <--- 405 has a digital root of 9 and it's odd!

Now, an odd number plus an even number is an odd number. 6 is an even number and is also a multiple of 3. If we add multiples of 6 to 405, we can find the other answers.

405 + 6n, where n is an integer, will give you the other answers (just make sure you don't go over 500).

Some of the answers are:

405 + 6(0) = 405 (any answer lower than this goes below 400)

405 + 6(1) = 411

405 + 6(2) = 417

405 + 6(3) = 423

405 + 6(4) = 429

...

405 + 6(14) = 489

405 + 6(15) = 495 (any answer higher than this goes above 500)