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I would not say that tests "measure logic": the fact is that logic is always unambiguous, that's its whole point. There is a certain set of facts from which absolutely unambiguous conclusions follow (there cannot be two solutions, there cannot be a "non-standard" solution, logic is always unambiguous, this is its power and meaning).
Items on an IQ test usually involve finding patterns in the given data: such items can have different solutions depending on the reasoning of the solver.
Let's give an example: let's say in the task they are asked to continue a series of numbers:
3 5 7 ?
the correct answer is most likely 3 5 7 9 (each next number is 2 more than the previous one).
We have Vasya, who writes "3 5 7 are odd prime numbers. The next odd prime number will be 11. The correct answer is 3 5 7 11". Why is Vasya wrong? Why is his rationale worse?
The LOGIC task does not allow different interpretations of the condition. IQ tests allow 2v31