There doesn't seem to be a universally accepted definition of what constitutes 'intelligence.'
The most I can do is approach the topic in a very roundabout way...
IQ VS. Intuition | Bryan Helmig
This is a fairly old post. Ignore the point the post is trying to make about intuition (I'll return to it in a moment) and focus on the 'IQ test question' examples provided.
[Situation 1] It is technically possible to answer all three questions correctly without the use of 'intelligence' if one reads the questions very carefully, translates them into logical formulas and then works through them mechanically. For example, the formula for the first question is
x+(1+x) = 1.10, where
x is the price of the ball. This is not an exercise in intelligence, and could arguably be learned to an extent (one of the criticisms of IQ testing). 'Intuition' is completely excluded from this process.
The post (and the study it refers to) paints intuition in a pretty poor light. However, consider a scenario in which someone reads the ball question and 'intuitively' conclude that the answer is 10 cents.
Why is it that most(?) people are content to write down the (incorrect) answer and move on to the next question [Situation 2], whereas others will have the gut feeling of
'wait a minute... this isn't right!' and re-read the question, possibly transitioning over to the mechanical method to determine the answer. [Situation 3]
Situation 1 and situation 3 may both result in a correct answer.
but is situation 3 not also an exercise in 'intuition'?
The difference between the way intuition manifests in situation 2 vs situation 3, is what I think intelligence is, and its use isn't limited to hypothetical test questions.
Think of the times when you know something is right or wrong (or missing something crucial) before you actually work through it rationally. And when you do, it turns out that your first feeling was correct.
(One of the) problems with IQ tests is that at the end, what it measures is whether you got the questions right -- not whether you exercised intelligence to do so.
Learned knowledge (situation 1) can provide you with the correct answers but it is not the same as intelligence.