Hi!
You can certainly solve this type of problem by applying divisibility rules, but like almost all data sufficiency yes-no number property problems, picking numbers is also an excellent approach.
When you pick numbers in data sufficiency, it's vital to follow 2 steps:
1) pick a number (or numbers) that are "legal" (i.e. follow all the rules provided); and then
2) plug the number (or numbers) back into the question, trying to get both a yes and a no answer.
Since we need to get both a yes and a no to show that a statement is insufficient, you'll always have to pick at least 2 sets of numbers.
Applying picking numbers to this question:
andersonlgb wrote:
If n is a positive integer, is n+4 divisible by 8?
(1) n+12 is divisible by 8
(2) n is divisible by 12
From the stem, we know that n is a positive integer, but nothing else. To the statements:
1) 16 is divisible by 8, so let's pick n=4 so that n+12 is divisible by 8.
If n=4, is n+4 divisible by 8? YES
Now we pick another value for n to try to get a "no" answer.
24 is the next number divisible by 8, so let's pick n=12 so that n+12 is divisible by 8.
If n=12, is n+4 divisible by 8? YES
We've gotten a yes answer for 2 consecutive values of n; at this point we can probably deduce that n+4 will always be divisible by 8: sufficient.
(If we're still not convinced, we would try one more value for n).
(2) n is divisible by 12.
Let's start with the obvious choice, n=12. If n=12, is n+4 divisible by 8? YES.
The next possible value of n is 24. If n=24, is n+4 divisible by 8? NO.
We've gotten a yes and a no answer, so (2) is insufficient - no further work required.
(1) is sufficient, (2) isn't, choose (A).
* * *
Here's a good general rule for attacking DS number property questions:
if the applicable rules jump out at you, then apply them to solve the question; and
if after 3-5 seconds of thought the rules aren't jumping out at you, dive in and pick numbers.
The one thing you can NEVER afford to do on test day is stare at the screen, hoping to have an epiphany - quite literally, every second you spend waiting for inspiration your score is going down.
