Data Sufficiency

Hello everybody!

I'm having some problems with divisibility problem such as this:

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

Anybody can tell me what is the correct way to attack this kind of problem? And how to solve this one specifically?

Thanks,

about this particular problem
is n+4 divisible by 8
(1) n+12=8k, n=8k-12, 8k-12+4=8k-8=8(k-1)-always divisible by 8, so suff
(2)n=12m, does 12m+4 divisible by 8
m=1, 12+4=16 divisible by 8
m=2, 24+4=28, not divisible by 8
as we have both yes and no answer, insuff
imo A

Tks!

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.