There is a girl who likes number 100 but doesn't like 99, she likes 900 but doesn't like 850, she likes 2500 but doesn't like 2600. I have to find out which number she is going to like.
The proposed solutions are:
$(a)\quad 3000\\ (b)\quad 4200\\ (c)\quad6400\\ (d)\quad 7600$
I don't know how to work out this problem to find the solution. Any help greatly appreciated.
As people in the comments found out, the correct answer is likely to emerge from finding a very simple pattern that matches the examples given. "She likes perfect squares" is thus a a fair reasoning, that yields to the answer (c) 6400 = $80^2$.
However, by fitting a polynomial to the data points given -and to one of the answers- I can find a rule that matches the given numbers she likes, and one arbitrary answer, while also not matching any other number.
My opinion on this matter is that no rigorous test should include such question. If anything, it awards a few students who will feel smart by quickly guessing a simple pattern, while others have no direct method for finding a solution. And the test designer better hope no one comes up with a simple enough pattern that matches a different answer, such as "The number of circles in the numbers must be less than the number of digits." which would match (a), (c) and (d), and sounds more like a child's reasoning.
One may also argue that questions like these are traps, designed to cause immature students to waste precious time on a question that seems easy but may take indefinitely long to find an answer, due to the lack of a direct and well defined solution method. In other words, good students are expected to either find a solution very quickly or decide to skip the question.