1) Find the sum of the digits of the next number of the sequence: 1, 5, 19, 49, 101, ?
Choices are: 7, 8, 10, 12
2) Find the next element of the sequence: 2/4; 3/12; 5/30; 7/56; ?
Choices are: 9/81, 9/90, 10/100, 11/110.
3) Find the nex letter in the sequence: B, C, E, H, J, K, ?
Choices are: T, N, Ñ, V.
Ñ comes after N and before O in the Spanish alphabet, if anyone was wondering.
I have solved the first and second ones, but I still think the reasoning to get the answers is bad. I have no idea of the third, similar methods to the other ones give nothing useful.
For the second one, if you take those elements as fractions and simplify, you get 1/2, 1/4, 1/6, 1/8. If you consider the numerators, they're 2, 3, 5, 7, apparently a list of prime numbers. So the next one has 11 as numerator and simplifies to 1/10, the answer is 11/110.
The third one, no idea. The position of the letters are 2, 3, 5, 8, 10, 11. Doing the thing with the substraction gives 1, 2, 3, 2, 1. The pattern is complete, and continuing with 0 would give K as an answer, not valid. Assuming the patten is just 5 long and repeat, the next number is 2, which would give an M, another invalid choice. There's also no pattern that I could recognize with the names of the letters, and that would be cheap anyway.
The problem is that with the given information (which is just the elements in order) I can't justify the validity of my methods. The first one only works if the numbers are produced by evaluating consecutive numbers in a polynomial of low enough degree (three in this case). The second method works because I could recognize a particular sequence. If I had attended that class I'd probably be able to reproduce a method for the third problem. But then, what is the test measuring? Is it really logical thinking, or just the ability to solve pattern recognition tests with a specific mindset? None of those methods could do anything if the sequence was exponential, or obtained via modular arithmetics or a high degree polynomial. The visual sequences are the same, you have to assume they're formed by following very simple patterns (rotations, cyclic permutations of elements...) and in general, you have to use very little data to extrapolate.
So, in short: Are these tests useful for measuring logical skills? Do they make good predictions for intelligente/grades? Is it even possible to get a single, logical answer in the third problem?