Please read this before asking "How many questions can I get wrong before I get a X score on the GMAT" or "is the first 10 questions more important than the later ones?"
our illustrious rhyme has written this dissertation on the algorithms. Based on the little I know, I think he's got it on the spot. So read on and just focus your test time on doing your best, double checking your answers, and moving on. Any second-guessing the system will only hurt you instead of help you.
This is a fundamental misunderstanding to how adaptive tests work.
The first few questions do not count more than the last few.
The number you get wrong is meaningless. You could get 15 wrong and score 700, it wouldn't matter (there will be some upper limit .. at some point you have to get something right to score well)
Its WHICH questions you get wrong that matter.
I wish I could find my post from ages ago that describes how this works in detail, unfortunately I can't.
Oh wait... here it is...
The super short version: There is a bell curve. The system figures out where you sit on it. In 37 questions, you can't "fool it".
The longer version: Here it is in a nutshell.. The GMAT develops a confidence interval around your score. In the beginning this score is wide - say, 500 to 600, as you answer questions, two things happen - one, it tightens the band (550 to 575 say) and it changes the actual estimate (say 571). (Think raw scores if you want) Eventually it tries to get to a point where the probability of getting a question right is .5 - that is your "estimated ability" is precisely in the middle of a standard normal curve, and around that is a very narrow band - a confidence interval of your score (the variance decreases, think basic stats.. Few numbers with large ranges vs lots of data points with trending singularity - variance decreases over time with each q answered).
The bottom line is this: whether or not you get the first question right or wrong doesn't matter because by the time you get to 37, it will have "snuffed" you out. Moreover, how many questions you get right doesn't matter either (again, within reason, if you get all 37 wrong then yea, it matters) - its WHICH questions you get right. This is the critical thing to remember - its not whether or not you get one right ... its whether or not you got one with P < .5 right. Getting a "600" level question right (where for you p(correct) = .5)) is not the same as getting a "700" level question right.
Put it this way. I could get every single question at 600 right and NEVER get a 700 question right. No matter whether I end up getting 20 questions right and 10 700 questions wrong, my score isn't going to get to 700. Similarly, I could get 29 questions right, and 1 question wrong - if that question I got wrong was a 700 score question, I'm not getting a 700.
Make sense? Think about a bell curve that keeps getting tighter... So where was I ? Oh yea... Moreover, the software is using a bell curve, not a retarded monkey, to figure out your score. So getting one wrong doesn't decrease your score by 20 points and getting one right increase it by 20. If it did, it would be very very easy to figure out your score (see later how
Kaplan and others make this insanely stupid assumption in their materials). What happens of course is that it takes an amalgamation of data points to determine the move in your score - your previous responses, the level of difficulty of that particular question, the confidence interval and variance expected around your "True" ability, the probability estimate for your true ability at a given question etc... All of this helps it decide how far to move your score up and down....
But the key to realize here - and this is the key - is that the band of scores you get continues to get TIGHTER AND TIGHTER with every question - while it keeps shifting up and down trying to gather data. Fundamentally, after 37 questions its shifted a bunch and the band has become narrow. Whether or not you got the first question right or wrong really doesnt matter.
Now for more detail:
Imagine each question with a bell curve of correct answers based on your true ability level. That is, each question has a known difficulty level. There is an expected number of right answers for people with true ability level of X and a percent of expected correct answers at Y.
I'm going to steal graphs from another site to make the point.
http://img485.imageshack.us/img485/5043/j225a322tn.jpgIn this graph, based on my previous response, the probability of getting this right is roughly 80% at this particular skill level. Ignore the bottom numers OK? Those aren't supposed to be a gmat score specifically. Think of "500" as ability level 3. Maybe a 600 is ability level 3.42.
As I answer a question the system figures out my "true" ability level estimate. This is based on the bell curves of the questions I got right and the inverse of the questions I got wrong.
So, lets say my true ability level is "4.0", an the GMAT ranks ability levels from 0 to 5. It'll hand me an ability level question of 2.5 to start, to guage my true ability.
At this point, the GMAT will do a few things:
1) It will update my ability estimate based on my answer.
2) It will determine the confidence interval for this ability estimate
So maybe we start out here:
http://img485.imageshack.us/img485/9021/j225a338sk.jpgBut then we end up here:
http://img140.imageshack.us/img140/9544/j471a135cp.jpgThe black line is my current estimated ability, the red my true ability and the yellow banded area is a confidence
interval.
As I answer questions, the estimated ability level comes towards the true level:
http://img140.imageshack.us/img140/3223/j471a233yx.jpgBut how does it decide what to show me?
http://img140.imageshack.us/img140/3191/j471a219dn.jpgAs I answer questions, the software uses its current estimate of your score by evaluating questions avaliable around that band and selects the one most appropriate.
As we keep doing this the confidence interval will continue to move - tighter and tighter.
Until eventually, the interval decreases:
http://img140.imageshack.us/img140/5456/j471a738yb.jpgThis is basically how the GMAT works, though from what I understand it comes to it's true ability estimate by meshing the curves as well, so the intervals get very small by the 37th question.
This doesnt mean the first questions are worth more... it means you are more likely to get an overly difficult or overly easy problem in the first ten questions because the band in which - the confidence interval of questions to pick from - is still wide... but the way it changes its own estimates will depend on the questions you get but they do NOT impact your score more than other questions.
The reason people seem to think this is because they sway more, so if you get a really easy one wrong early on, it might give you a really really question and set your ability level low, but this is only temporary as BY DEFINITION, the exam's purpose is to narrow that band to your natural ability.
By definition the exam is going to continue to give you questions to get your probability level to .5 on each question - this will give a nice confidence band and a good indication of you true ability.
Kaplan and Princeton all argue the first few questions argue more. The whole premise of their argument lies in the ridiculously simplified concept of a graph that looks like this:
http://img149.imageshack.us/img149/5439 ... ive1uh.gifThis, however makes NO SENSE. The sap getting hard questions right would quickly see his score increase, yes, but would very quickly hit a probability of .5, in which case he would flatten out. The person who saw their score decrease, would, of course get an easier question on #2, but based on their true ability, they would also be increased on subsequent correction questions - each question modifies the software's estimate of your true ability. The probabiliy of getting an easier question goes up, but so does the p that it is answered correctly..
In fact, if you really want to get into it....
One can just as equally argue that, in the begining the software is wildly guessing - and lets say that you just get lucky and get 5 really Oops hard questions right. The software has 32 more questions to find your true ability. It will. If on the other hand, you END WITH 5 extremely hard questions that you get right, the software may have found your true ability by question 32 - in which the 5 you randomly got correct by luck, have increased your overall score. Woot!
But do you see it? It goes the other way too...
Lets say you get hte first 10 right. The machine thinks you are a 750er. You think it wont adjust that by the time you get to question 37? Now think. What happens if you get the first 10 right, and the last 10 wrong? By then, its narrowed your estimated ability yes, but with each incorrect answer (after the first), you begin to widen that band again - and the software will readjust your true ability estimate downwards. The confidence levels will remain tight but your overall score has still decreased just as if you ahd taken the first 10 and gotten them wrong.
The only difference here is whether the questions sets become exhausted or less than ideal at a given level - unlikely as hell on the gmat - but even if the software is forced to give you less than p=.5 q's, it would still effectively continue to drop your score approriately - and proportionally.
In other words,
Question 1 is just as important as question 37.