Are IQ tests "beatable"?
Short answer:
Yes, but it does not matter    

Long answer:
Each question has some inner mechanism that you either know or you don't. Usually you should know how to do it, but you don't know, that you should do it that way. Once you know the right method, next puzzle you would solve much faster - most IQ tests are like this. If you don't know the mechanism, it could be very hard to solve - IQ tests should be like this.
For example this one - once you know, that there are 4 squares all the time, next puzzle of this kind will be much easier. Most puzzles use Subtraction and Addition - once you try this two things, you will solve lots of IQ tests. You are expected to know this methods, and that it will be used in test.
Problem with IQ tests is insufficient number of respondents - since it needs lots of people to create norm.
For example I created test with possible score 0-100, and 50% of people reached 80 points. When you take the test and had 80 score, your IQ should be 100. But when (because of better education for example) most scores begin to be above 80, norm will change and for 100IQ you would have to score 82 or more.     

So yes, you can study for it, but when more and more people do it (and knows about using subtraction, 4 squares all the time and so), norm will change and tests would be harder for everyone anyway, since there will be always exactly 50% of people that could reach at least 100IQ. ( = take some online tests, since most people do it, otherwise it would put you into disadvantage.)    

Sources:
Flynn effect  - raise in IQ due to education and also health (notice not genes).
More about norm
Tests commonly used - in it you can hide math operations without using numbers.