k: {-4,-3,-2,-1,0,1,2,3,4,5,6,7}
positive integers are 1,2,3,4,5,6,7
range = largest - smallest = 7-1 = 6
IMO B

Good question - dealing with ranges and actual numbers can be a little tricky, and this question makes you deal with it twice. They tell you it's 12 consecutive numbers starting at -4, but does that mean you just add 12? And then once you get the highest positive number, you have to get the range and not just that number.

The "rule" is that, for inclusive sets (you're counting all numbers in the set and not just the numbers in between the highest and lowest), the number of values is equal to the range-plus-one. And for exclusive sets it's the range-minus-one.

But I'm a huge fan of the idea that it's crucial to know that the rule exists, but much less crucial to know exactly what it is. By the very nature of the fact that it's a rule, you can prove it with small numbers even if you don't have it memorized verbatim - if it's a rule, it will hold regardless of what set of eligible numbers you use.

Here, my concerns would be 1) that I'm not sure how the number of values will necessarily translate to the range, and 2) that we're going from negative to positive and that 0 could play an odd role here. As a GMAT test-taker, numbers with different properties (negative, 0, positive, etc.) tend to heighten my awareness so that I don't fall into any traps. So I might try this - using the set of numbers -1, 0, and 1:

-there are 3 numbers
-but the range is 2
-and it goes from negative to positive so it's analogous to the -4 and 12 straight integers situation

That tells me that I'd need to subtract one from the number of values to get the range. So 12 values means a range of 11, and so I'd have -4 through 7.

And because the range of 1 through 7 (the positive integers) is 7-1 = 6, the correct answer is 6.


Now...on this problem, like cans did, you can probably just list out all 12 numbers quickly enough that overthinking it may waste more time than just gutting it out. But had they given a much wider range (K consists of 53 consecutive integers, of which -9 is the least integer...) then you may want to prove the situation to yourself with smaller numbers and extrapolate the results to the larger numbers given in the question. It's a decent strategy to have at your disposal...