Which number completes the series? 3, 6, 11, 18, 27, …
If you tried doubling here it failed immediately, and that failure is the useful part of the question. Where you go next is what the item is really testing.
Fluid intelligence and second order patterns
The answer is 38. The gaps between the terms are 3, 5, 7 and 9, which are the odd numbers in order, so the next gap is 11 and 27 plus 11 gives 38.
What makes this harder than question two is that the rule is not in the numbers themselves. It is in the differences between them. You have to notice that the first pattern failed, step back a level and look for a pattern in the pattern.
Psychologists call this kind of reasoning fluid intelligence: solving a novel problem without relying on stored knowledge. It is the ability that peaks earliest in life and it is the one people most want to improve.
Can you actually get smarter?
This is the question everyone asks about intelligence, and the honest answer has two halves that point in opposite directions.
Partly, and less than the advertising suggests. Training programs that promise to raise general intelligence tend to produce large gains on the trained task and very little that carries over to anything else. That result has held up across a lot of studies.
What does improve, and improves a great deal, is crystallized intelligence: the knowledge and strategies you accumulate. A person with deep knowledge of a field solves problems in it faster than a person with more raw processing power and no background, every time.
- When the obvious rule fails, look at the differences rather than the terms
- Write the gaps underneath the series instead of computing them mentally
- Watch for the simple sequences hiding one level down: odds, evens, squares
- Invest in depth in one field rather than general brain training
If depth beats general training, the practical question becomes which depth is worth building. Our guide on how to pick skills worth your time covers how to value a skill against what you already know. It opens in a new tab.
Question seven is famous, and most people who answer it quickly get it wrong.