Learn by Novus · Open practice pack v1

Abstract reasoning: patterns, rules and transformations: open practice pack: worked explanations

100 untimed questions across 10 authored sections.

This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.

Worked explanations

abstract-reasoning-s01-q01

The sequence simply alternates between two shapes, so after a circle the square returns.

abstract-reasoning-s01-q02

The three sizes cycle in a fixed order, so after medium the cycle continues with large.

abstract-reasoning-s01-q03

Each step skips exactly one letter of the alphabet, so G is followed by I.

abstract-reasoning-s01-q04

Each group adds one more star than the last, so three stars are followed by four.

abstract-reasoning-s01-q05

The arrow rotates a quarter turn clockwise each step through a four-direction cycle, so after right it points down.

abstract-reasoning-s01-q06

The repeating block is two black dots followed by one white dot, so the white dot is due next.

abstract-reasoning-s01-q07

Each step moves two letters backwards through the alphabet, so T is followed by R.

abstract-reasoning-s01-q08

The three symbols repeat in a fixed cycle, and the cycle has reached the sun's turn.

abstract-reasoning-s01-q09

The side count climbs 3, 4, 5, so the next shape has six sides, a hexagon.

abstract-reasoning-s01-q10

Each group has twice as many dots as the one before, so 8 doubles to 16.

abstract-reasoning-s02-q01

Three of the shapes are built entirely from straight sides; the circle is the only curved shape.

abstract-reasoning-s02-q02

X, K and T are drawn with straight strokes only, while S is drawn entirely with curves.

abstract-reasoning-s02-q03

A, H and M each have a vertical line of symmetry, their left and right halves mirror each other, but F does not.

abstract-reasoning-s02-q04

Cube, sphere and cylinder are solid three-dimensional forms; the square is a flat two-dimensional shape.

abstract-reasoning-s02-q05

Three of the pairs repeat the same letter twice; only one pairs two different letters.

abstract-reasoning-s02-q06

Three codes place a letter before its matching digit; one reverses the order and puts the digit first.

abstract-reasoning-s02-q07

The triangle, pentagon and heptagon have odd numbers of sides (3, 5, 7); the hexagon's six sides make it the only even one.

abstract-reasoning-s02-q08

B, D and H sit at alphabet positions 2, 4 and 8, each double the last, while K sits at position 11.

abstract-reasoning-s02-q09

Three groups contain exactly three identical symbols; the star group contains only two.

abstract-reasoning-s02-q10

S, N and Z look the same after a half-turn (180° rotation), but E does not share this rotational symmetry.

abstract-reasoning-s03-q01

Track each feature separately: the shape alternates, so a square is due; the colour cycle red-blue-green has reached green.

abstract-reasoning-s03-q02

The cycle is three directions long (up, right, down), and after up the cycle continues with right.

abstract-reasoning-s03-q03

Three hours past 9 wraps around the clock face back to 12, completing the four-step cycle.

abstract-reasoning-s03-q04

The sequence alternates between a fixed A and a letter that advances one step each visit (B, C, D), so E is due.

abstract-reasoning-s03-q05

The two features run at different speeds: the triangle flips every step (so ▼ is due) while the shading holds for two steps (so black continues).

abstract-reasoning-s03-q06

The cycle is four symbols long, so position 10 = two full cycles (8) plus 2 more, the second symbol of the cycle.

abstract-reasoning-s03-q07

Position 12 is exactly four complete cycles of three, so it lands on the final term of a cycle.

abstract-reasoning-s03-q08

The shapes alternate circle/square while the count rises by one each pair, so three squares follow three circles.

abstract-reasoning-s03-q09

The pendulum passes through the centre between every swing to a side, so centre always follows left or right.

abstract-reasoning-s03-q10

Run the two cycles separately: the letter cycle X-Y-Z has reached Y, and the case alternation has reached lower case.

abstract-reasoning-s04-q01

Each group adds two dots to the last, so 7 grows to 9.

abstract-reasoning-s04-q02

The pattern loses two blocks each step, so 4 shrinks to 2.

abstract-reasoning-s04-q03

The amount added grows by one each step (+1, +2, +3, +4), so the next step adds 5 to reach 16.

abstract-reasoning-s04-q04

Each count is twice the one before, so 16 doubles to 32.

abstract-reasoning-s04-q05

Each count is half the one before, so 8 halves to 4.

abstract-reasoning-s04-q06

Two rules alternate: double, then subtract one. After doubling 9 to 18, the next step subtracts one to give 17.

abstract-reasoning-s04-q07

The counts are square grids of side 1, 2, 3, 4, so the next grid is 5 × 5 = 25 dots.

abstract-reasoning-s04-q08

Each triangle adds a new bottom row one dot longer than the last (+2, +3, +4), so the next step adds 5 to reach 15.

abstract-reasoning-s04-q09

The rule alternates +3 then −2. After adding 3 to reach 10, the next step subtracts 2 to give 8.

abstract-reasoning-s04-q10

Adding the last two counts, 5 + 8, gives 13.

abstract-reasoning-s05-q01

The relationship enlarges the shape without changing it, so the square simply becomes large.

abstract-reasoning-s05-q02

b and d are left-right mirror images of each other, and the mirror image of p is q.

abstract-reasoning-s05-q03

The number names how many sides the shape has, and the six-sided shape is the hexagon.

abstract-reasoning-s05-q04

The relationship swaps the shading from black to white while keeping the shape the same.

abstract-reasoning-s05-q05

The relationship reverses the order of the two symbols, so CD becomes DC.

abstract-reasoning-s05-q06

The relationship turns a flat shape into its three-dimensional counterpart, and the solid built from squares is the cube.

abstract-reasoning-s05-q07

The relationship doubles the first number, and 5 doubled is 10.

abstract-reasoning-s05-q08

The relationship moves two places forward in the alphabet, and two letters after M comes O.

abstract-reasoning-s05-q09

The relationship swaps the roles of the two symbols: the outer symbol moves to the middle and vice versa.

abstract-reasoning-s05-q10

The relationship moves the last symbol to the front of the group, so the star leads the two squares.

abstract-reasoning-s06-q01

Reversing writes the symbols in the opposite order, so the last letter comes first.

abstract-reasoning-s06-q02

Only the outer symbols trade places, 2 and 9 swap, while the middle symbols 5 and 8 stay put.

abstract-reasoning-s06-q03

Each symbol is written twice in place before moving to the next, following the worked example exactly.

abstract-reasoning-s06-q04

The operator keeps the 1st, 3rd and 5th symbols and drops the 2nd and 4th, just as in the worked example.

abstract-reasoning-s06-q05

Each letter moves forward exactly one place: C to D, F to G, K to L.

abstract-reasoning-s06-q06

Work from the inside out: swapping first and last turns ABC into CBA, then doubling each symbol gives CCBBAA.

abstract-reasoning-s06-q07

Each rotation moves the front symbol to the back: WXYZ becomes XYZW, then XYZW becomes YZWX.

abstract-reasoning-s06-q08

Follow the cycle one step at a time: the circle first becomes a square, and the square then becomes a triangle.

abstract-reasoning-s06-q09

Reversing 1234 gives 4321, and removing the first symbol of that result leaves 321.

abstract-reasoning-s06-q10

The original string XY is followed by its reverse YX, producing a mirror-symmetric result.

abstract-reasoning-s07-q01

Each row must contain all three shapes exactly once, and the circle is the one still missing from row 3.

abstract-reasoning-s07-q02

Moving one cell to the right adds one dot, so the middle cell holds 4 + 1 = 5 dots.

abstract-reasoning-s07-q03

Each row shifts the previous row one place to the left, so row 3 continues white, black, grey, and grey also completes its column.

abstract-reasoning-s07-q04

Combining the two cells overlays their contents, and a vertical line laid over a horizontal line forms a cross.

abstract-reasoning-s07-q05

Columns 2 and 3 already have their single star, so row 3's star must occupy the only remaining column.

abstract-reasoning-s07-q06

The side count rises 5, 6 along the row, so the final cell holds the seven-sided heptagon.

abstract-reasoning-s07-q07

A quarter turn clockwise carries a left-pointing arrow round to point up.

abstract-reasoning-s07-q08

Applying the stated rule to the bottom-right cell gives 3 × 3 = 9 dots.

abstract-reasoning-s07-q09

The square appears in both cells so it is excluded, leaving the circle and triangle, which each appear only once.

abstract-reasoning-s07-q10

Row 3 already has large and small, so medium completes the row, and it also completes the third column, which holds large and small so far.

abstract-reasoning-s08-q01

Two strands alternate: 1, 2, 3, 4 and 10, 20, 30. The next term belongs to the tens strand.

abstract-reasoning-s08-q02

One strand climbs from the start of the alphabet (A, B, C) while the other descends from the end (Z, Y, X); the climbing strand is due next.

abstract-reasoning-s08-q03

Triangle groups (growing by one) alternate with advancing letters, and it is the triangles' turn with four.

abstract-reasoning-s08-q04

The odd positions climb by two (2, 4, 6, 8) and the even positions climb by three (3, 6, 9); the next term continues the threes with 12.

abstract-reasoning-s08-q05

The letter strand steps back two places each time (Z, X, V, T) while the number strand doubles; the letters are due next with R.

abstract-reasoning-s08-q06

The shapes alternate circle/square while the count rises by one each term, so six squares follow five circles.

abstract-reasoning-s08-q07

The odd positions hold square numbers (1, 4, 9, 16) and the even positions simply count (2, 3, 4, 5); the next square number is 25.

abstract-reasoning-s08-q08

The letters advance two places each step while the digits climb through the odd numbers, giving I paired with 9.

abstract-reasoning-s08-q09

Three strands rotate (a count, a letter, then a dot group that grows by one), and it is the dots' turn with three.

abstract-reasoning-s08-q10

One strand falls by ten (100, 90, 80, 70) while the other doubles (1, 2, 4, 8); the falling strand is due next.

abstract-reasoning-s09-q01

Each example reverses the order of the digits, so 39 becomes 93.

abstract-reasoning-s09-q02

The machine shifts every letter one place forward in the alphabet, so P, Q, R become Q, R, S.

abstract-reasoning-s09-q03

Each output is three times the input plus one, a rule all three examples satisfy, so 9 maps to 28.

abstract-reasoning-s09-q04

The machine repeats only the final symbol, so XY gains a second Y.

abstract-reasoning-s09-q05

Each output is the sum of the input's digits (2+5=7, 6+3=9, 4+8=12), so 5+7 gives 12.

abstract-reasoning-s09-q06

The machine halves the number of dots, so eight dots become four.

abstract-reasoning-s09-q07

Each example removes one side from the shape, so the seven-sided heptagon becomes a six-sided hexagon.

abstract-reasoning-s09-q08

Each output is the pair's product plus two (2×3+2=8, 3×4+2=14, 4×5+2=22), so 5×6+2 gives 32.

abstract-reasoning-s09-q09

Each output is the letter's position in the alphabet, and Q is the 17th letter.

abstract-reasoning-s09-q10

The machine accepts numbers that read the same forwards and backwards, and only 45654 is such a palindrome.

abstract-reasoning-s10-q01

Reversing 58274 gives 47285, and deleting that result's last symbol leaves 4728.

abstract-reasoning-s10-q02

Trace the wrap-around jumps one at a time: 1 to 4, 4 to 7, 7 to 2, 2 to 5, and finally 5 to 8.

abstract-reasoning-s10-q03

Apply the alternating rules in order: 5 doubles to 10, minus 3 is 7, doubles to 14, minus 3 is 11.

abstract-reasoning-s10-q04

Shifting A, C, E forward two places gives C, E, G; reversing that intermediate result gives G, E, C.

abstract-reasoning-s10-q05

Each double flip cancels itself out, so only the three single flips matter: an odd number of flips turns white to black, whatever the order.

abstract-reasoning-s10-q06

Two quarter turns clockwise make a half turn, and a half turn points a left-facing arrow to the right.

abstract-reasoning-s10-q07

The gaps between terms double each step (+1, +2, +4, +8), so the next gap is +16, giving 34.

abstract-reasoning-s10-q08

The gaps grow by two each step (+4, +6, +8, +10), so the next gap is +12, giving 42.

abstract-reasoning-s10-q09

Handle each symbol type with its own rule: D and H step back to C and G, while 3 and 5 double to 6 and 10.

abstract-reasoning-s10-q10

Doubling AB gives AABB, and keeping the 1st and 3rd symbols of that result restores the original AB, the two operators undo each other.