The problem I had was with plugging in 0 for K.
2(0) + 1 = 1 0x1x2 = 0 (Is 0 divisible by 4? This was my biggest problem because it was the only example that wasn't stated in the Number Properties book!)
yes, 0 is divisible by 4 - and, as the poster below has noted, by any other positive integer you care to divide by. 0 is divisible by every positive integer.
note the following:
way you will encounter this sort of query is if you plug in your own numbers
. in other words, the official problems WILL NOT require you to decide the issue of whether 0 is divisible by n
(for whatever n
); they restrict the scope of divisibility problems strictly to positive divisors and positive dividends.
however, you should still know this fact, because, as you have seen here, you will often encounter "extra" questions like this as artifacts of plugging in your own numbers. therefore, even though the gmat won't test the concept directly, you may still have to rely on it to solve the problem because of your number plugging.
as long as we're at it, if you encounter "negative multiples" in your number plugging adventures, then yes, those are divisible too. for instance, -4 is divisible by 4, as are -8, -12, and the whole lot.