Mensa practice test

What this practice set is, and is not

IQ Octopus is not affiliated with or endorsed by Mensa, and this is not a Mensa test or a copy of one. It is ten original reasoning puzzles in the nonverbal style that many high-range tests favor, weighted toward the harder end. There are no easy warm-ups: the set starts at medium and the second half is hard.

Mensa accepts people who score at or above the 98th percentile, the top 2%, on an approved, supervised standardized test (Mensa International). Nothing you take online counts toward that, here or anywhere else. American Mensa, for example, does not accept unsupervised or internet-based tests, but accepts scores from about 200 standardized tests given by professionals (American Mensa: qualifying scores). See the Mensa admission test, explained.

The puzzles in this set

Six 3x3 matrices

Matrices are the backbone of the set. Medium grids combine two rules; hard ones combine up to three, such as a count that rises across each row, a shape that appears once per row and column, and a fill that is fixed per row. Some grids run their rules down the columns instead of across the rows. Line-overlay grids keep only the lines that appear in exactly one of the first two tiles of a row.

Two sequences

At this level a sequence usually stacks two changes, for example a turn of an eighth clockwise plus a fill that cycles through solid, outlined and hatched. Find both from the first two tiles and confirm on the next pair.

Two figure analogies

A changes into B by one or two transformations: a turn, a flip, a new fill, a size change, or small shapes being added, removed, moved around the edge or swapped with the main shape. Apply exactly those to C.

How to work harder puzzles

On hard items, the gap between a good and a poor result is mostly discipline, not insight. Three habits do most of the work:

1. Write the rules in words. “Count up by one across, shape is a distribution of three, fill per row.” Holding three rules in your head is where errors creep in; naming them keeps them separate.
2. Predict before you look. Build the missing tile from the rules, then go to the options. Every wrong option breaks exactly one rule, so a vague prediction leaves you choosing between two or three near twins.
3. Eliminate by rule. Take the rule you are surest of and cross off every option that breaks it. Then the next rule. You often reach the answer before you are sure of the hardest rule.

A hard grid, worked

Picture this. Row one: a large circle, a large square, a large star, all hatched. Row two: a square, a star, a circle, all solid. Row three: a star, a circle, and a gap, all outlined. Three rules are at work. Each row has its own fill (hatched, solid, outlined). Each shape appears once in every row and every column. And every tile is large. The gap needs the shape its row and its column are missing: row three has a star and a circle, and the third column already has a star and a circle, so the missing tile is a square. The answer is a large outlined square.

The options will include a large solid square (fill from the wrong row), a large outlined circle (shape repeated), and a small outlined square (size broken). Each breaks one rule, which is why naming all three first pays off.

Timing

You get 30 seconds per puzzle, five minutes for the set. Hard matrices in 30 seconds are tight on purpose: they show you whether your method is fast enough yet. If the ring empties, the item counts as unanswered and the next one loads. If you consistently run out of time, slow down and practice untimed on the hard matrix puzzles, which show the worked solution for every grid.

What the 98th percentile looks like on different scales

The qualifying line is a percentile, not a fixed number, because different tests use different scales. On a scale with a mean of 100 and standard deviation 15, the 98th percentile works out to about 131. Older Stanford-Binet forms used standard deviation 16, and the Cattell Culture Fair III scale uses 24 (Wikipedia: IQ classification). That is why Mensa UK quotes qualifying scores of 148 on Cattell III B and 132 on the Culture Fair test, which are both the 98th percentile on those scales (Mensa UK). The top 2% page shows the line on the bell curve.

Reading your practice score

You will see a count out of ten and a description of that practice performance. Please do not read it as a pass or a fail. Ten items cannot estimate where you sit relative to the 98th percentile, and they are not normed against any population. A strong result tells you the format suits you. A weaker one most often means the stacked rules need practice, which is fixable.

How much does practice help?

Familiarity with a test format does raise scores. A review of retesting studies found an average gain of about a quarter of a standard deviation, roughly 4 IQ points, and more when the same form was taken again (Hausknecht et al., 2007). Near a cutoff, that is a meaningful amount, which is why it is worth knowing the formats before a supervised session. Practice on fresh puzzles rather than retaking the same ten.

Next steps

For a direct answer on qualifying scores, read what IQ you need for Mensa. For an estimate of where you stand before you book a supervised test, take the full IQ Octopus test: it reports an estimated IQ with a percentile and a confidence range. It is an online estimate and cannot be used for Mensa admission, but it can tell you whether the top 2% looks within reach. The Raven's matrices practice test gives you ten more grids.