IQ Test Questions: Examples, Answers and What They Measure

Which questions are on which IQ test?

The named tests differ mainly in length and format: Mensa’s online tests have 33 to 35 puzzles, the WAIS-5 has 7 subtests for its Full Scale IQ, and IQMog has 20 matrix items.

The Mensa IQ Challenge page and the Mensa Norway page give the same item count, the same time limit and the same named creator. Only the Norwegian page describes the format.

What does a matrix question look like, and how do you solve it?

A matrix question shows a 3×3 grid with the bottom-right cell missing, and you choose the option that follows the same rules as the other eight cells. Raven’s Progressive Matrices made the format famous, and most online tests copy it.

Here is an original item, written for this page, in words instead of pictures. Each cell lists what it contains.

1. Read the first row alone. The shape stays a circle and the count goes up by one: 1, 2, 3.
2. Check the second row. It holds squares, counting 2, 3, 4. The count again rises by one along the row, and the shape changed from circles to squares.
3. Read the columns. Column 1 counts 1, 2, 3 going down, column 2 counts 2, 3, 4, and column 3 starts 3, 4. Each column also grows by one.
4. Apply both rules to the missing cell. The third row is triangles, and the count after 3 and 4 is 5.
5. Check the options. The answer is C, 5 triangles.

The habit that helps most is to find the rule in one row, then confirm it in a second row before you look at the options. The pattern guide lists the common rule types, such as rotation, shading and shape combination.

How do number and letter series questions work?

A series question gives a row of numbers or letters that follows one hidden rule, and you supply the next item. The Mensa Deutschland quiz opens with eight of these, tasks 1 to 8 of 33.

Number series example

Find the next number: 4, 7, 13, 25, 49, ?

1. Write the gaps between neighbours: 3, 6, 12, 24.
2. The gaps double each time, so the next gap is 48.
3. Add it to the last number: 49 + 48 = 97.

Letter series example

Find the next letter: B, D, G, K, P, ?

1. Turn letters into places in the alphabet: B is 2, D is 4, G is 7, K is 11, P is 16.
2. The gaps are 2, 3, 4, 5. They grow by one each step.
3. The next gap is 6, and 16 + 6 = 22. The 22nd letter is V.

When the gaps look random, test two other ideas. Check whether each number is multiplied by the same amount, and check whether two separate series are woven together. In 3, 20, 6, 17, 9, 14, ? the odd positions go up by 3 and the even positions go down by 3, so the next number is 12.

What questions are on the Mensa test?

The free Mensa tests online are practice, and the admission questions are not public. Mensa International says that unsupervised online tests cannot be used for admission.

Membership needs a pass at or above the 98th percentile on an approved test that was properly administered and supervised, according to the Mensa International FAQ. Supervision is the deciding factor: British Mensa offers a proctored online test, while the free tests in the table are unsupervised practice.

That is why a search for Mensa test questions and answers leads to practice material: the Mensa IQ Challenge and the Mensa Deutschland quiz are free, and the American Mensa practice test is a paid, 30-minute online test that is copyrighted and confidential. Work through them for the question types, then take the supervised test.

An answer key would not help you for long. Mensa International says it is in the final stages of implementing computerised adaptive testing, which selects items from a large item bank, so there is no answer key that could be leaked. For the score rules, read what Mensa requires for admission.

Does practicing IQ test questions raise your score?

Practice raises your score on the same kind of test, and the gain is larger when you see the identical questions again. It does not show that your reasoning ability changed.

A 2007 meta-analysis by Hausknecht and colleagues pooled 107 samples and 134,436 people who took a cognitive ability test twice. Scores rose by an adjusted 0.26 standard deviations on average. The median gap between sittings was 20 days, and the mean sample age was 19.

So if you have seen the questions before, your score will probably be a little higher next time, on average. Individual results vary with sleep, attention and ordinary measurement error, and some people score lower. The authors also predict that the extra gain from an identical form fades over time and matches the alternate-form gain after just under two years.

A gain on a familiar format reflects familiarity with the format. To get the most from practice, read how to prepare for an online IQ test.

Why don’t professional IQ tests publish their questions?

Professional IQ tests keep their questions private because prior exposure can inflate a score and make it harder to interpret.

Mensa Deutschland puts it this way: real intelligence tests are more varied and extensive than its quiz, and candidates must not know the tasks beforehand. It concludes that there are no serious real intelligence tests on the internet, according to its online quiz page.

Access is controlled as well. The WAIS-5 has qualification level C, so Pearson sells it to qualified professionals, and the American Mensa practice test is copyrighted and confidential. The Hausknecht figures show why it matters: on average, seeing the identical form again was worth about 3 more IQ points than seeing a different one.

Free online question sets give you an estimate of how you handle one kind of puzzle, and a fast way to find the question types worth practicing.

Which questions does IQMog use?

IQMog uses 20 fixed matrix puzzles, each with a 3×3 grid, one missing cell and four answer choices. Everyone gets the same 20 items.

The items were made with RAVEN-FAIR, an open-source generator described in a CVPR 2021 paper by Benny, Pekar and Wolf. Those authors built it because the earlier RAVEN dataset from 2019 “selects the negative examples in a way that is easily exploited”.

Here is the exploit in plain terms. If every wrong option is the right answer with one detail changed, the right answer is the one that most options resemble. In the triangle item above, option C differs by one detail from A, B and D, and no other option does. You could pick C without reading the grid.

In the RAVEN-FAIR paper, a model that never saw the puzzle picked the right answer from the eight RAVEN options 80.17% of the time, against 12.5% by chance. On RAVEN-FAIR it managed 17.24%. That test used eight choices and a computer model, and IQMog shows four choices, so the figures describe the generator and not our form.

Each right answer moves the estimate by 3 points on a 70 to 130 scale, with a score range and percentile next to it, and the scoring method is public. 20 of 20 correct gives 130, the top of the scale. You get the result in about 10 minutes and can use it to see where you stand before a supervised Mensa test.