Wow that is incredible that you are able to understand, "each term from x subscript 1 to x subscript k is 3 greater than the previous term, and each term from x subscript k + 1 to x subscript n is 3 less than the previous term, where n and k are positive integers and k < n. If x subscript 0 equals x subscript n equals 0 and if x subscript k equals 15, what is the value of n?"
When I read this, I am still confused. What is this math jargon and how are you able to read this?
Truthfully - and I don't say this to be condescending - I would say this is fairly typical of describing a mathematical sequence, as far as language goes. It's just how math is written verbally. To me, it's just a matter of exposure, which means you just have to do more problems. I find that one place the modern education system does a poor job is helping students to make good connections between our natural language and mathematical language. There is too much focus on just chugging through batteries of exercises instead of applications from verbal prompts.
I also find it helps if you take the word problem bit by bit. If you do this, you'll realize there isn't really much jargon in that passage. We wouldn't typically expect much jargon to appear on the GMAT, being the college aptitude test as it is. More than likely, it's that you didn't encounter a great deal about sequences in your high school math courses (correct me if I'm wrong); which indicates you just need to keep doing more and more practice. The more time you spend actually reading math problems and working them, the more natural the language becomes.
First, what do we know from the passage? (Establish what the passage gives you as identities: "this equals this")
x
0 = 0
x
k = 15
x
n = 0
k < n
From that, you can answer your very first question in this thread. If the subscript k < n in the sequence, but the value stored at x
k is greater than the value stored at x
n, then you know the sequence will go up to the value at k (15) and then back down to the value at n (0).
What is the passage asking?
It wants to know the value of the subscript n, at x
n. Therefore, it is interested in what step in the sequence this is.
Let's continue.
"Each term from x1 to xk is 3 greater than the previous term."
So how could we describe that relationship mathematically?
With the rule:
xy+1 = xy + 3
So, x
1 = x
0 + 3, (or 3)
x
2 = x
1 + 3, (or 6)
x
3 = x
2 + 3, (or 9)
You can see that each of the values stored at each additional subscript is just going to be a multiple of 3. You might also notice it is equal to:
3 * subscript, such that we can make a faster rule where
xy = 3 * y
Since you know that x
k = 15, then 15 = k * 3, and simplifying:
k = 5. So x
k=5 = 15.
The passage then tells you that,
"each term from xk+1 through xn is three less than the previous term."
That means that x
6 will equal 3 less than x
k=5, so on and so forth until you get to x
n. You could go through writing out the rule like we did before and thinking through it that way, and this would be just fine. But the thing to realize is that since x
n = 0, then we are going from 15 back to 0 by the same absolute value of increment: 3 (it's just in the negative direction this time).
If getting to 15 required k = 5, then getting back to 0 by the same steps in reverse will require
k * 2, or 10.
n = 10
Once you get more familiar with reading problems like this, it will take you 30 seconds to do all of this thinking and arrive at the answer.
