Simple Divisibility

[Guest]

If x is an integer divisible by 15 but not divisible by 20, then x
CANNOT be divisible by which of the following?

6
10
12
30
150

Can anybody tell me how the answer is C?

[Paul]

This is how I solve it.

Since X is divisible by 15, you can include 3 and 5 into the X's prime box.
Then, if X is not divisible by 20 which has (2, 2, 5), then you know that X's prime box can't have (2, 2)

So now you go ahead and look which answer choice has (2, 2) as it's primes:
6 (2, 3)
10 (2, 5)
12 (2, 2, 3) - aha, bingo!
30 (2, 3, 5)
150 (2, 3, 5, 5)

So now you have pin pointed the answer (12), which has two of 2's.

Enjoy

[esledge]

Paul's prime box method is the fastest and easiest.

Here's another way, just so you have a backup:

x is divisible by 15, so x could be 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, etc. (just list enough to see a pattern)
x is NOT divisible by 20, so cross 60, 120, 180, etc. off the list (see the pattern of multiples of 60)
Therefore, x could be (15, 30, 45), (75, 90, 105), (135, 150, 165), etc.

You can find at least one number on that list that is divisible by 6 (e.g. 30), 10 (e.g. 30), 30 (e.g. 30) and 150 (e.g. 150).
None of the numbers on the list are divisible by 12.