Abstract, numerical, verbal and spatial reasoning, from easy to hard, with every answer explained.
Each question is a different type, and each links to a guide that teaches the method behind it. Work at your own pace: there is no timer here, and nothing you pick is recorded.
The questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
Work rows first, one attribute at a time (see the matrix lesson):
- Constant in a row — every cell in a row uses the same shape; the shape changes only between rows.
- Progression — the figure grows by one size step at each cell, left to right (small → medium → large).
Apply each rule to the bottom row and the missing cell must be a large outlined diamond.
Convert letters to alphabet positions (A=1 … Z=26) and the pattern shows itself: two series are interleaved: 1st/3rd/5th letters move +2, 2nd/4th/6th letters move +3. Positions: 5, 17, 7, 20, 9, 23 → next position 11 = K.
In exactly one option, the two figures are the SAME figure rotated. Which option?
Reveal the answer
The answer is B.
Show why — the worked reasoning
Every option shows two figures with the same number of squares, so counting proves nothing — the question is whether one figure can be TURNED onto the other. Give the figure a landmark (the longest straight edge, or the single square that juts out) and ask what the landmark's neighbours look like going clockwise around the outline: turning never changes that order. In three options the two figures are mirror images — their outlines read in opposite order, so only lifting one off the page would match them. In one option a single square has moved. In one — the answer — the two figures are the same shape at different angles.
Track each attribute separately along the strip:
- The shading cycles outlined → hatched → solid.
Apply every change once more to the fourth cell and only one option matches the result.
Every shape of the same kind weighs the same. Using the balanced scales, how many shapes are needed to balance the last one?
▲⚖■■
■■⚖●●●
▲▲▲▲⚖? × ●
Every scale is balanced. How many ● balance the shapes on the last scale?
Reveal the answer
The answer is C — 12.
Show why — the worked reasoning
Every scale is an equation, so you can rewrite one shape in terms of another and substitute along the chain. The scales give 1▲ = 2■, 2■ = 3●. Follow them through and 4▲ is worth exactly 12●. Work one scale at a time and always in the same direction — the classic error is inverting a ratio partway along, which lands you on the reciprocal answer.
All vrintors are crelors. All crelors are vrelors. Which conclusion must be true?
Reveal the answer
The answer is B — All vrintors are vrelors..
Show why — the worked reasoning
Draw the categories as circles (a set diagram) and encode each premise: "All X are Y" nests X inside Y; "No X are Y" separates the circles; "Some" pins at least one member in the overlap. Test each option against every diagram the premises allow — a conclusion only follows if no allowed diagram breaks it. Here, All vrintors are vrelors. holds in every case; each other option can be drawn false without violating a premise. (The words are nonsense on purpose: judge only the logic, never plausibility.)
When the net is folded into a cube, which symbol is on the face OPPOSITE the
?
Reveal the answer
The answer is B.
Show why — the worked reasoning
Pick any face as the base and fold the neighbours up mentally — or use the shortcut: on a net, two faces are opposite when they are separated by exactly one face in a straight line, or sit two apart around a corner strip. Folding this net, the triangle and the diamond never share an edge — they end up on opposite faces. Every other option shares an edge with the asked face somewhere on the net, so it folds into an adjacent face, not the opposite one.
Name the transformation that turns A into B before looking at the options: change the size by 2 step(s) in the small→medium→large cycle. Apply exactly the same transformation to C. The shape itself never changes — only the attributes listed. Distractors repeat C unchanged, repeat B, or apply the transformation twice.
Find the rule linking each pair before touching the options. Test simple rules in order — add/subtract, multiply, multiply-then-add, square. Here the rule is: subtract 9 (15 → 6). Applying it to 4: -5.
In a certain code, CHAIR is written as FKDLU, and every letter has moved the same number of places forward through the alphabet (past Z it carries on from A). How many places is that?
Reveal the answer
The answer is D — 3.
Show why — the worked reasoning
Turn the letters into alphabet positions and subtract. C is 3 and became F = 6, a move of 3 places forward (counting on past Z and round to A when the count runs off the end). Confirm on a second letter: H = 8 → K = 11, again +3. The answer is 3. Counting the other way round gives 23: the same landing letters, but that is a move backward, and the question asks how far forward.
The sheet is folded and punched as shown. Unfolded, which pattern results?
Reveal the answer
The answer is D.
Show why — the worked reasoning
Work backwards, one unfold at a time. The sheet was folded (the top half is folded down onto the bottom), then punched. Each unfold mirrors every existing hole across that fold line and ADDS the mirrored copy — so 1 punch(es) through 2 layers become 2 holes. Traps: forgetting one unfold (too few holes), mirroring across the wrong line, or leaving the holes unmirrored.
Scan one attribute at a time — shape, then shading, then size, then dots — and count values as you go. Four of the five figures share the same shape; exactly one differs on it. The other attributes are decoys: every one of their values appears on at least two figures, so none of them can single a figure out. The odd one out is the figure with the different shape.
Dana is lighter than Mara. Dana is heavier than Omar. Who is the heaviest?
Reveal the answer
The answer is D — Mara.
Show why — the worked reasoning
Sketch the order as a chain while reading, placing each person relative to the others. The statements pin down: Mara > Dana > Omar (reading “>” as “heavier”). So the answer to “Who is the heaviest?” is Mara. If a statement only repeats known facts, skip it; if two orders were possible, the correct answer would be “cannot be determined”.
Turning a figure never makes a mirror image of it. Exactly one option here IS a mirror image of the figure — which one?
Reveal the answer
The answer is E.
Show why — the worked reasoning
Turning a figure never changes its handedness; reflecting it always does. That is the whole question here, and the mirror image has been turned as well, so you cannot spot it by looking for a left-right flip. Trace the outline of the target from its top-left square and note the turn sequence (left, left, right…). Every option that is only rotated repeats that sequence exactly; the mirror image repeats it with left and right exchanged. One option is reversed but has a square in a different place — count squares before you commit.
Each box always applies the same hidden rule, shown by its worked examples. What comes out of the pipeline?
→▲→
→▲→
→▲→
?
Reveal the answer
The answer is E.
Show why — the worked reasoning
Induce each box's rule from its two worked examples — a rule must explain BOTH examples, not just one. Here box ▲ swaps the shape for the next one in the cycle (circle → square → triangle → circle). Then push the new input through the boxes in order, transforming one attribute at a time. The wrong options each skip exactly one box or apply the last box twice — check every attribute against your predicted result.
Every copy of a symbol has the same value. What is the value of the asked symbol?
■■▲20▲■■20▲▲■19192020
▲ = ?
Reveal the answer
The answer is C — 6.
Show why — the worked reasoning
Treat each row as an equation over the icon values. Start from the row (or pair of rows) that isolates one icon — for example, rows differing by a single symbol give that symbol's value by subtraction. Substitute back until every icon is known. The queried icon works out to 6. The traps are off-by-one arithmetic slips — verify your values against EVERY row total before answering.
On this island every person either always tells the truth or always lies. Tomas says: “Dana and Kofi are both truth-tellers.” Dana says: “Mara is a liar.” Kofi says: “Mara and Dana are both truth-tellers.” Mara says: “Kofi is a truth-teller.” How many of them are liars?
Reveal the answer
The answer is E — 3.
Show why — the worked reasoning
Test one assumption at a time. Suppose a person is a truth-teller — then their statement must be true; suppose they are a liar — then their statement must be false. Push each assumption through everyone else's claims and keep only the arrangement that never contradicts itself. Exactly one arrangement survives: Tomas = liar, Dana = truth-teller, Kofi = liar, Mara = liar, so 3 of them are liars. The usual slip is to stop at the first arrangement that fits the first two claims — always carry it through to the last one.
How many cubes are in this stack, counting the ones you cannot see?
Reveal the answer
The answer is B — 10.
Show why — the worked reasoning
Count column by column, not cube by cube: every stack you can locate contributes its FULL height, including cubes hidden behind or below the ones you see — a cube can't float, so anything supporting a visible cube must exist. The stacks here are 2 + 2 + 2 + 1 + 1 + 2 cubes tall, giving 10 in total. The classic mistake is counting only visible faces, which loses the hidden supporters.
The free test has 20 questions across abstract, numerical, verbal and spatial reasoning. It takes 12 minutes, needs no sign-up, and explains every answer.
They are the same kinds of question IQ-style tests use, made by the same generators and answer checkers as The IQ Gym's question bank. They are written for this page and are never used in a test, so seeing their answers here gives nothing away.
Can these questions tell me my IQ?
No. A count of right answers on practice questions is not a score: these questions are not normed and there is no clock. For an estimate, the free test has 20 timed questions and reports a range rather than a single number.
Will practising raise my IQ?
Practice makes you faster and more accurate on the question types you train, and that can lift your score on a test that uses them. Research on practice effects finds the gains stay with the trained kinds of task rather than raising general intelligence, and The IQ Gym does not claim otherwise.
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