kevincan wrote:
This need not be an AP- a sequence is simply a list of numbers in a definite order
I agree with this, and the answer is 5. Trying to use too many mathematical principles can kill a gmat question. Sometimes, it's just brute force that gets the right answer. I prefer to do a sequence out a few times, look for patterns, and then go to the answer.
Look at this question. It says that a1 is -30, so using the given formula, a2 must be either -25, -24, -23. All good and well, but now we have three numbers to go off of for a2. If we try it for all of them, we see that a2 can be either -20, -19, -18, -17, -16. There are now 5 possibilities.
Keep doing it out for a few more. You will see that each term grows in the number of possibilities by 2. So a3 will have 7 possible answers, a4 will have 9, etc.
Then you just need to figure out the first possible number for each term, which is always based on the previous first possible number, and then get a range.
So, since a3 started with -20, the smallest number for a4 is -15, and there are 7 terms, so the range is -15 to -9.
a5: smalles term, based on a3, is -10. 9 terms, so range is -10 to -2.
a6: 11 terms, range: -5 to +5
a7: 13 terms, range: 0 to 12
a8: 15 terms, range 5 to 19
a9: 17 terms, range 10 to 26
a10: 19 terms, range 15 to 33
a11: 21 terms, range 20 to 40
a12: 23 terms, range 25 to 47 <-- this is the first k!
a13: 25 terms, range 30 to 54 <-- 2nd k
a14: 27 terms, starting with 35 <-- 3rd k
a15: 29 terms, starting with 40 <-- 4th k
a16: 31 terms, starting with 45 <-- 5th k
a17: 33 terms, starting with 50 <-- no more k!
So there are 6 possible k's that work, thus the answer is 5.
That said, this is too much work for the gmat. I would never expect to see it there.