What is in this logical reasoning test?

Twenty questions with four answers each: ten number series where you find the next number, and ten short sets of statements where you pick the conclusion that follows. They run from easy to hard.

What is a good score?

We do not publish a pass mark or a comparison with other people. Too few people have taken this test to say anything about averages. Your result is how many of the twenty you got right, which you can compare with your own score next time.

No. Your answers stay on this page and are gone when you close it. We do not ask for an account and we do not count your score.

Logical reasoning test: 20 practice questions with answers (free)

Twenty questions with four answers each: find the next number in a series, or pick the conclusion that must follow from a few statements. Pick your answers, press the check button and you see how many are right, with the right answer under every question you missed.

How this logical reasoning test works

Every question has one right answer. In a number series the wrong answers are the numbers you get from the most common wrong rule, such as repeating the last step. In a set of statements they are the usual slips: turning a rule around, or concluding more than the statements say. Guessing blind earns you about a quarter right. A question left empty counts as a miss. All twenty questions were written for this page.

Number series

Start with the differences between neighbouring numbers. If they are equal, as in 5, 8, 11, 14, the series adds the same step each time. If they grow by one each time, as in 4, 5, 7, 10, 14, the step itself goes up. If the differences do not show a pattern, try the ratios: 3, 6, 12, 24 doubles each time. Some series use two rules in turn, so check whether every second number follows one rule and the others a different one.

Conclusions from statements

The question is what must be true if the statements are true, and not what is likely. Take the statement "If the alarm sounds, the doors lock" and the fact that the doors are unlocked. The alarm cannot be sounding, because it would have locked them. Turn the rule around and you go wrong: locked doors do not prove that the alarm sounded. Words such as "some", "all", "none" and "only" carry the weight, so read them twice.

When nothing follows

Some sets of statements leave the question open. If the choir members can read music and some people who read music play the piano, you cannot tell whether any choir member plays the piano. An answer that says so is a legitimate answer, and in this test it is sometimes the right one.

Practising

Do one round, check it, and write down the rule behind each question you missed before you try again. The list is fixed, so a better result next time may mean you remember the answers. It is a quick check of how you work through a problem and says nothing about how clever you are.

More to try

For synonyms, opposites and short passages, try the verbal reasoning test. If you prefer a puzzle without questions, there is sudoku, and the brain games page has five short games.