{ "format": "novus-learn-open-practice", "version": 1, "packId": "cognitive-skills-abstract-reasoning", "source": "cognitive-skills", "slug": "abstract-reasoning", "title": "Abstract reasoning: patterns, rules and transformations: open practice pack", "subtitle": "100 untimed questions across 10 authored sections.", "sourceHref": "/cognitive-skills/abstract-reasoning", "disclaimer": "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.", "worksheet": { "title": "Learner worksheet", "instructions": [ "Every pattern in this bank is described in words, so all the information you need is in the prompt itself. Work at a comfortable pace. The aim is to notice the rule, not to race the clock.", "Choose one answer for each item. For a delayed-recall item, read its study text, cover it, and then answer without looking back." ], "groups": [ { "id": "abstract-reasoning-s01", "title": "Continuing simple sequences", "instructions": "Spot the single repeating or stepping rule and choose what comes next.", "items": [ { "id": "abstract-reasoning-s01-q01", "prompt": "A sequence runs: circle, square, circle, square, circle. What comes next?", "choices": [ { "id": "a", "label": "Circle" }, { "id": "b", "label": "Square" }, { "id": "c", "label": "Triangle" }, { "id": "d", "label": "Star" } ] }, { "id": "abstract-reasoning-s01-q02", "prompt": "A shape repeats in three sizes: small, medium, large, small, medium. What comes next?", "choices": [ { "id": "a", "label": "Small" }, { "id": "b", "label": "Medium" }, { "id": "c", "label": "Large" }, { "id": "d", "label": "Extra large" } ] }, { "id": "abstract-reasoning-s01-q03", "prompt": "A letter sequence runs: A, C, E, G. Which letter comes next?", "choices": [ { "id": "a", "label": "I" }, { "id": "b", "label": "H" }, { "id": "c", "label": "J" }, { "id": "d", "label": "K" } ] }, { "id": "abstract-reasoning-s01-q04", "prompt": "A star pattern grows: ★, ★★, ★★★. Which group comes next?", "choices": [ { "id": "a", "label": "★" }, { "id": "b", "label": "★★" }, { "id": "c", "label": "★★★" }, { "id": "d", "label": "★★★★" } ] }, { "id": "abstract-reasoning-s01-q05", "prompt": "An arrow turns through the sequence: up, right, down, left, up, right. Which direction comes next?", "choices": [ { "id": "a", "label": "Up" }, { "id": "b", "label": "Down" }, { "id": "c", "label": "Left" }, { "id": "d", "label": "Right" } ] }, { "id": "abstract-reasoning-s01-q06", "prompt": "A dot pattern runs: ●, ●, ○, ●, ●, ○, ●, ●. What comes next?", "choices": [ { "id": "a", "label": "○" }, { "id": "b", "label": "●" }, { "id": "c", "label": "●●" }, { "id": "d", "label": "○○" } ] }, { "id": "abstract-reasoning-s01-q07", "prompt": "A letter sequence runs backwards through the alphabet: Z, X, V, T. Which letter comes next?", "choices": [ { "id": "a", "label": "S" }, { "id": "b", "label": "Q" }, { "id": "c", "label": "R" }, { "id": "d", "label": "P" } ] }, { "id": "abstract-reasoning-s01-q08", "prompt": "A symbol sequence runs: moon, star, sun, moon, star, sun, moon, star. What comes next?", "choices": [ { "id": "a", "label": "Moon" }, { "id": "b", "label": "Star" }, { "id": "c", "label": "Cloud" }, { "id": "d", "label": "Sun" } ] }, { "id": "abstract-reasoning-s01-q09", "prompt": "A shape sequence gains one side each step: triangle, square, pentagon. Which shape comes next?", "choices": [ { "id": "a", "label": "Heptagon" }, { "id": "b", "label": "Octagon" }, { "id": "c", "label": "Hexagon" }, { "id": "d", "label": "Circle" } ] }, { "id": "abstract-reasoning-s01-q10", "prompt": "A dot pattern doubles each step: 1 dot, 2 dots, 4 dots, 8 dots. How many dots come next?", "choices": [ { "id": "a", "label": "10 dots" }, { "id": "b", "label": "16 dots" }, { "id": "c", "label": "12 dots" }, { "id": "d", "label": "24 dots" } ] } ] }, { "id": "abstract-reasoning-s02", "title": "Odd one out: classifying by a shared rule", "instructions": "Find the feature three of the four share, then pick the one that breaks it.", "items": [ { "id": "abstract-reasoning-s02-q01", "prompt": "Which of these shapes does not belong with the other three?", "choices": [ { "id": "a", "label": "Square" }, { "id": "b", "label": "Triangle" }, { "id": "c", "label": "Rectangle" }, { "id": "d", "label": "Circle" } ] }, { "id": "abstract-reasoning-s02-q02", "prompt": "Which of these capital letters does not belong with the other three?", "choices": [ { "id": "a", "label": "S" }, { "id": "b", "label": "X" }, { "id": "c", "label": "K" }, { "id": "d", "label": "T" } ] }, { "id": "abstract-reasoning-s02-q03", "prompt": "Which of these capital letters does not belong with the other three?", "choices": [ { "id": "a", "label": "A" }, { "id": "b", "label": "H" }, { "id": "c", "label": "F" }, { "id": "d", "label": "M" } ] }, { "id": "abstract-reasoning-s02-q04", "prompt": "Which of these does not belong with the other three?", "choices": [ { "id": "a", "label": "Cube" }, { "id": "b", "label": "Square" }, { "id": "c", "label": "Sphere" }, { "id": "d", "label": "Cylinder" } ] }, { "id": "abstract-reasoning-s02-q05", "prompt": "Which of these letter pairs does not belong with the other three?", "choices": [ { "id": "a", "label": "AB" }, { "id": "b", "label": "XX" }, { "id": "c", "label": "AA" }, { "id": "d", "label": "MM" } ] }, { "id": "abstract-reasoning-s02-q06", "prompt": "Which of these codes does not belong with the other three?", "choices": [ { "id": "a", "label": "A1" }, { "id": "b", "label": "B2" }, { "id": "c", "label": "C3" }, { "id": "d", "label": "4D" } ] }, { "id": "abstract-reasoning-s02-q07", "prompt": "Which of these shapes does not belong with the other three?", "choices": [ { "id": "a", "label": "Triangle" }, { "id": "b", "label": "Hexagon" }, { "id": "c", "label": "Pentagon" }, { "id": "d", "label": "Heptagon" } ] }, { "id": "abstract-reasoning-s02-q08", "prompt": "Which of these letters does not belong with the other three?", "choices": [ { "id": "a", "label": "B" }, { "id": "b", "label": "D" }, { "id": "c", "label": "K" }, { "id": "d", "label": "H" } ] }, { "id": "abstract-reasoning-s02-q09", "prompt": "Which of these symbol groups does not belong with the other three?", "choices": [ { "id": "a", "label": "★★" }, { "id": "b", "label": "▲▲▲" }, { "id": "c", "label": "●●●" }, { "id": "d", "label": "■■■" } ] }, { "id": "abstract-reasoning-s02-q10", "prompt": "Which of these capital letters does not belong with the other three?", "choices": [ { "id": "a", "label": "S" }, { "id": "b", "label": "N" }, { "id": "c", "label": "E" }, { "id": "d", "label": "Z" } ] } ] }, { "id": "abstract-reasoning-s03", "title": "Alternating and repeating cycles", "instructions": "These patterns repeat in fixed cycles. Work out the cycle length before answering.", "items": [ { "id": "abstract-reasoning-s03-q01", "prompt": "In a sequence, the shape alternates circle/square while the colour cycles red, blue, green. So far: red circle, blue square, green circle, red square, blue circle. What comes next?", "choices": [ { "id": "a", "label": "Red square" }, { "id": "b", "label": "Green circle" }, { "id": "c", "label": "Green square" }, { "id": "d", "label": "Blue square" } ] }, { "id": "abstract-reasoning-s03-q02", "prompt": "An arrow cycles: up, right, down, up, right, down, up. Which direction comes next?", "choices": [ { "id": "a", "label": "Up" }, { "id": "b", "label": "Right" }, { "id": "c", "label": "Down" }, { "id": "d", "label": "Left" } ] }, { "id": "abstract-reasoning-s03-q03", "prompt": "A marker on a clock face jumps three hours clockwise each step: 12, 3, 6, 9. Where does it land next?", "choices": [ { "id": "a", "label": "3" }, { "id": "b", "label": "6" }, { "id": "c", "label": "9" }, { "id": "d", "label": "12" } ] }, { "id": "abstract-reasoning-s03-q04", "prompt": "A letter sequence runs: A, B, A, C, A, D, A. Which letter comes next?", "choices": [ { "id": "a", "label": "E" }, { "id": "b", "label": "A" }, { "id": "c", "label": "F" }, { "id": "d", "label": "B" } ] }, { "id": "abstract-reasoning-s03-q05", "prompt": "In a sequence, the triangle flips each step while the shading changes every two steps. So far: black ▲, black ▼, white ▲, white ▼, black ▲. What comes next?", "choices": [ { "id": "a", "label": "White ▼" }, { "id": "b", "label": "Black ▲" }, { "id": "c", "label": "Black ▼" }, { "id": "d", "label": "White ▲" } ] }, { "id": "abstract-reasoning-s03-q06", "prompt": "The four suits repeat in a fixed order: ♠, ♥, ♦, ♣, ♠, ♥, ♦, ♣, and so on. Which symbol is 10th in the sequence?", "choices": [ { "id": "a", "label": "♠" }, { "id": "b", "label": "♥" }, { "id": "c", "label": "♦" }, { "id": "d", "label": "♣" } ] }, { "id": "abstract-reasoning-s03-q07", "prompt": "The numbers 1, 2, 3 repeat forever: 1, 2, 3, 1, 2, 3, … What is the 12th term?", "choices": [ { "id": "a", "label": "3" }, { "id": "b", "label": "1" }, { "id": "c", "label": "2" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "abstract-reasoning-s03-q08", "prompt": "A pattern runs: ●, ■, ●●, ■■, ●●●. What comes next?", "choices": [ { "id": "a", "label": "●●●●" }, { "id": "b", "label": "■■" }, { "id": "c", "label": "●●●" }, { "id": "d", "label": "■■■" } ] }, { "id": "abstract-reasoning-s03-q09", "prompt": "A pendulum pattern runs: left, centre, right, centre, left, centre, right. What comes next?", "choices": [ { "id": "a", "label": "Left" }, { "id": "b", "label": "Right" }, { "id": "c", "label": "It cannot be determined" }, { "id": "d", "label": "Centre" } ] }, { "id": "abstract-reasoning-s03-q10", "prompt": "A sequence cycles the letters X, Y, Z while alternating upper and lower case: X, y, Z, x, Y, z, X. What comes next?", "choices": [ { "id": "a", "label": "Y" }, { "id": "b", "label": "y" }, { "id": "c", "label": "z" }, { "id": "d", "label": "x" } ] } ] }, { "id": "abstract-reasoning-s04", "title": "Growing and shrinking patterns", "instructions": "Work out how much the pattern grows or shrinks at each step. The step size itself may change.", "items": [ { "id": "abstract-reasoning-s04-q01", "prompt": "A dot pattern grows: 1 dot, 3 dots, 5 dots, 7 dots. How many dots come next?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "8" }, { "id": "c", "label": "10" }, { "id": "d", "label": "11" } ] }, { "id": "abstract-reasoning-s04-q02", "prompt": "A block pattern shrinks: 10 blocks, 8 blocks, 6 blocks, 4 blocks. How many blocks come next?", "choices": [ { "id": "a", "label": "3" }, { "id": "b", "label": "0" }, { "id": "c", "label": "1" }, { "id": "d", "label": "2" } ] }, { "id": "abstract-reasoning-s04-q03", "prompt": "A tile pattern grows: 1, 2, 4, 7, 11. How many tiles come next?", "choices": [ { "id": "a", "label": "15" }, { "id": "b", "label": "16" }, { "id": "c", "label": "14" }, { "id": "d", "label": "18" } ] }, { "id": "abstract-reasoning-s04-q04", "prompt": "A cell pattern doubles: 2, 4, 8, 16. How many cells come next?", "choices": [ { "id": "a", "label": "24" }, { "id": "b", "label": "20" }, { "id": "c", "label": "32" }, { "id": "d", "label": "30" } ] }, { "id": "abstract-reasoning-s04-q05", "prompt": "A dot pattern halves: 64, 32, 16, 8. How many dots come next?", "choices": [ { "id": "a", "label": "6" }, { "id": "b", "label": "2" }, { "id": "c", "label": "0" }, { "id": "d", "label": "4" } ] }, { "id": "abstract-reasoning-s04-q06", "prompt": "A counter pattern runs: 3, 6, 5, 10, 9, 18. What comes next?", "choices": [ { "id": "a", "label": "17" }, { "id": "b", "label": "36" }, { "id": "c", "label": "19" }, { "id": "d", "label": "20" } ] }, { "id": "abstract-reasoning-s04-q07", "prompt": "Dots are arranged in ever-larger square grids: 1 dot, 4 dots, 9 dots, 16 dots. How many dots come next?", "choices": [ { "id": "a", "label": "20" }, { "id": "b", "label": "24" }, { "id": "c", "label": "25" }, { "id": "d", "label": "36" } ] }, { "id": "abstract-reasoning-s04-q08", "prompt": "Dots are stacked in triangles, adding one more dot per new row: 1, 3, 6, 10. How many dots come next?", "choices": [ { "id": "a", "label": "14" }, { "id": "b", "label": "15" }, { "id": "c", "label": "16" }, { "id": "d", "label": "20" } ] }, { "id": "abstract-reasoning-s04-q09", "prompt": "A pattern rises and falls: 5, 8, 6, 9, 7, 10. What comes next?", "choices": [ { "id": "a", "label": "11" }, { "id": "b", "label": "9" }, { "id": "c", "label": "12" }, { "id": "d", "label": "8" } ] }, { "id": "abstract-reasoning-s04-q10", "prompt": "In a spiral pattern, each new count is the sum of the previous two: 1, 1, 2, 3, 5, 8. What comes next?", "choices": [ { "id": "a", "label": "13" }, { "id": "b", "label": "12" }, { "id": "c", "label": "16" }, { "id": "d", "label": "11" } ] } ] }, { "id": "abstract-reasoning-s05", "title": "Shape and symbol analogies", "instructions": "Work out how the first pair is related, then apply exactly the same relationship to the second.", "items": [ { "id": "abstract-reasoning-s05-q01", "prompt": "Small circle is to large circle as small square is to what?", "choices": [ { "id": "a", "label": "Large circle" }, { "id": "b", "label": "Large square" }, { "id": "c", "label": "Small triangle" }, { "id": "d", "label": "Large triangle" } ] }, { "id": "abstract-reasoning-s05-q02", "prompt": "The lower-case letter b is to d as p is to what? (Think of each pair as mirror images.)", "choices": [ { "id": "a", "label": "q" }, { "id": "b", "label": "g" }, { "id": "c", "label": "b" }, { "id": "d", "label": "o" } ] }, { "id": "abstract-reasoning-s05-q03", "prompt": "3 is to triangle as 6 is to what?", "choices": [ { "id": "a", "label": "Pentagon" }, { "id": "b", "label": "Octagon" }, { "id": "c", "label": "Heptagon" }, { "id": "d", "label": "Hexagon" } ] }, { "id": "abstract-reasoning-s05-q04", "prompt": "Black square is to white square as black circle is to what?", "choices": [ { "id": "a", "label": "White square" }, { "id": "b", "label": "Black triangle" }, { "id": "c", "label": "White circle" }, { "id": "d", "label": "Grey circle" } ] }, { "id": "abstract-reasoning-s05-q05", "prompt": "AB is to BA as CD is to what?", "choices": [ { "id": "a", "label": "CD" }, { "id": "b", "label": "DC" }, { "id": "c", "label": "CC" }, { "id": "d", "label": "DD" } ] }, { "id": "abstract-reasoning-s05-q06", "prompt": "Circle is to sphere as square is to what?", "choices": [ { "id": "a", "label": "Cylinder" }, { "id": "b", "label": "Pyramid" }, { "id": "c", "label": "Cone" }, { "id": "d", "label": "Cube" } ] }, { "id": "abstract-reasoning-s05-q07", "prompt": "3 is to 6 as 5 is to what?", "choices": [ { "id": "a", "label": "10" }, { "id": "b", "label": "15" }, { "id": "c", "label": "25" }, { "id": "d", "label": "8" } ] }, { "id": "abstract-reasoning-s05-q08", "prompt": "A is to C as M is to what?", "choices": [ { "id": "a", "label": "N" }, { "id": "b", "label": "P" }, { "id": "c", "label": "O" }, { "id": "d", "label": "Q" } ] }, { "id": "abstract-reasoning-s05-q09", "prompt": "XOX is to OXO as ABA is to what?", "choices": [ { "id": "a", "label": "ABA" }, { "id": "b", "label": "AAB" }, { "id": "c", "label": "BAB" }, { "id": "d", "label": "BBA" } ] }, { "id": "abstract-reasoning-s05-q10", "prompt": "▲▲● is to ●▲▲ as ■■★ is to what?", "choices": [ { "id": "a", "label": "■★■" }, { "id": "b", "label": "■■★" }, { "id": "c", "label": "★★■" }, { "id": "d", "label": "★■■" } ] } ] }, { "id": "abstract-reasoning-s06", "title": "Symbol operators and transformations", "instructions": "Each item defines an operator in the prompt. Apply it exactly as described.", "items": [ { "id": "abstract-reasoning-s06-q01", "prompt": "The operator → reverses a string of symbols. What is KLM → ?", "choices": [ { "id": "a", "label": "KML" }, { "id": "b", "label": "LKM" }, { "id": "c", "label": "MLK" }, { "id": "d", "label": "MKL" } ] }, { "id": "abstract-reasoning-s06-q02", "prompt": "The operator ◇ swaps only the first and last symbols of a string. What is ◇ applied to 2589?", "choices": [ { "id": "a", "label": "9852" }, { "id": "b", "label": "5289" }, { "id": "c", "label": "8529" }, { "id": "d", "label": "9582" } ] }, { "id": "abstract-reasoning-s06-q03", "prompt": "The operator # doubles every symbol: #(AB) = AABB. What is #(XY)?", "choices": [ { "id": "a", "label": "XXYY" }, { "id": "b", "label": "XYXY" }, { "id": "c", "label": "XY" }, { "id": "d", "label": "YYXX" } ] }, { "id": "abstract-reasoning-s06-q04", "prompt": "The operator ∆ removes every second symbol: ∆(ABCDE) = ACE. What is ∆(PQRST)?", "choices": [ { "id": "a", "label": "QS" }, { "id": "b", "label": "PRT" }, { "id": "c", "label": "PQR" }, { "id": "d", "label": "QST" } ] }, { "id": "abstract-reasoning-s06-q05", "prompt": "A rule shifts each letter one place forward in the alphabet (A becomes B). Apply it to the letters C, F, K.", "choices": [ { "id": "a", "label": "D, G, L" }, { "id": "b", "label": "B, E, J" }, { "id": "c", "label": "D, G, K" }, { "id": "d", "label": "E, H, M" } ] }, { "id": "abstract-reasoning-s06-q06", "prompt": "The operator ◇ swaps the first and last symbols; the operator # doubles every symbol. What is #(◇(ABC))?", "choices": [ { "id": "a", "label": "AABBCC" }, { "id": "b", "label": "CBACBA" }, { "id": "c", "label": "CCBBAA" }, { "id": "d", "label": "AACCBB" } ] }, { "id": "abstract-reasoning-s06-q07", "prompt": "The operator ★ rotates a string one position left: ★(ABCD) = BCDA. What is ★(★(WXYZ))?", "choices": [ { "id": "a", "label": "XYZW" }, { "id": "b", "label": "ZWXY" }, { "id": "c", "label": "WXYZ" }, { "id": "d", "label": "YZWX" } ] }, { "id": "abstract-reasoning-s06-q08", "prompt": "A rule replaces shapes in a cycle: ○ becomes □, □ becomes △, and △ becomes ○. If the rule is applied twice to ○, what results?", "choices": [ { "id": "a", "label": "□" }, { "id": "b", "label": "△" }, { "id": "c", "label": "○" }, { "id": "d", "label": "◇" } ] }, { "id": "abstract-reasoning-s06-q09", "prompt": "The operator ! reverses a string; the operator @ removes the first symbol. What is @(!(1234))?", "choices": [ { "id": "a", "label": "432" }, { "id": "b", "label": "321" }, { "id": "c", "label": "234" }, { "id": "d", "label": "123" } ] }, { "id": "abstract-reasoning-s06-q10", "prompt": "The operator M appends a string's reverse to itself: M(AB) = ABBA. What is M(XY)?", "choices": [ { "id": "a", "label": "XYYX" }, { "id": "b", "label": "YXXY" }, { "id": "c", "label": "XXYY" }, { "id": "d", "label": "XYXY" } ] } ] }, { "id": "abstract-reasoning-s07", "title": "Matrix reasoning: rules across rows and columns", "instructions": "Each item describes a 3×3 grid. Find the rule running along its rows or columns to fill the gap.", "items": [ { "id": "abstract-reasoning-s07-q01", "prompt": "In a 3×3 grid, every row contains one circle, one square and one triangle in some order. Row 3 so far reads: square, triangle, blank. What fills the blank?", "choices": [ { "id": "a", "label": "Square" }, { "id": "b", "label": "Triangle" }, { "id": "c", "label": "Star" }, { "id": "d", "label": "Circle" } ] }, { "id": "abstract-reasoning-s07-q02", "prompt": "In a 3×3 grid, the number of dots in each row increases by one from left to right. Row 3 starts with 4 dots. How many dots are in its middle cell?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "5" }, { "id": "c", "label": "6" }, { "id": "d", "label": "7" } ] }, { "id": "abstract-reasoning-s07-q03", "prompt": "In a 3×3 grid, row 1 reads black, grey, white and row 2 reads grey, white, black. Row 3 reads white, black, blank. What shade fills the blank?", "choices": [ { "id": "a", "label": "Black" }, { "id": "b", "label": "White" }, { "id": "c", "label": "Grey" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "abstract-reasoning-s07-q04", "prompt": "In a 3×3 grid, the third cell of each row shows the first two cells' contents combined into one figure. Row 3's first cell holds a vertical line and its second cell holds a horizontal line. What does its third cell show?", "choices": [ { "id": "a", "label": "A cross (both lines together)" }, { "id": "b", "label": "A vertical line only" }, { "id": "c", "label": "A horizontal line only" }, { "id": "d", "label": "An empty cell" } ] }, { "id": "abstract-reasoning-s07-q05", "prompt": "In a 3×3 grid, each row and each column contains exactly one star. The stars sit at row 1 column 2 and row 2 column 3. In which column is row 3's star?", "choices": [ { "id": "a", "label": "Column 2" }, { "id": "b", "label": "Column 3" }, { "id": "c", "label": "Any column" }, { "id": "d", "label": "Column 1" } ] }, { "id": "abstract-reasoning-s07-q06", "prompt": "In a 3×3 grid, shapes gain one side moving left to right along each row. Row 3 reads: pentagon, hexagon, blank. What fills the blank?", "choices": [ { "id": "a", "label": "Octagon" }, { "id": "b", "label": "Hexagon" }, { "id": "c", "label": "Heptagon" }, { "id": "d", "label": "Nonagon" } ] }, { "id": "abstract-reasoning-s07-q07", "prompt": "In a 3×3 grid, arrows rotate 90° clockwise moving left to right along each row. Row 3's first arrow points left. Where does its middle arrow point?", "choices": [ { "id": "a", "label": "Right" }, { "id": "b", "label": "Up" }, { "id": "c", "label": "Down" }, { "id": "d", "label": "Left" } ] }, { "id": "abstract-reasoning-s07-q08", "prompt": "In a 3×3 grid, the number of dots in each cell equals its row number multiplied by its column number. How many dots are in the bottom-right cell (row 3, column 3)?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "6" }, { "id": "c", "label": "8" }, { "id": "d", "label": "12" } ] }, { "id": "abstract-reasoning-s07-q09", "prompt": "In a 3×3 grid, the third cell of each row shows only the shapes appearing in exactly one of the first two cells. Row 3's first cell holds a circle and a square; its second cell holds a square and a triangle. What does its third cell show?", "choices": [ { "id": "a", "label": "A square only" }, { "id": "b", "label": "A circle and a triangle" }, { "id": "c", "label": "A circle, a square and a triangle" }, { "id": "d", "label": "A square and a triangle" } ] }, { "id": "abstract-reasoning-s07-q10", "prompt": "In a 3×3 grid, every row and every column contains one small, one medium and one large shape. Row 1 reads small, medium, large; row 2 reads medium, large, small. Row 3 reads large, small, blank. What size fills the blank?", "choices": [ { "id": "a", "label": "Small" }, { "id": "b", "label": "Large" }, { "id": "c", "label": "Medium" }, { "id": "d", "label": "It cannot be determined" } ] } ] }, { "id": "abstract-reasoning-s08", "title": "Interleaved sequences: two patterns in one", "instructions": "Each sequence weaves two or more independent strands together, separate them before answering.", "items": [ { "id": "abstract-reasoning-s08-q01", "prompt": "A sequence runs: 1, 10, 2, 20, 3, 30, 4. What comes next?", "choices": [ { "id": "a", "label": "40" }, { "id": "b", "label": "5" }, { "id": "c", "label": "35" }, { "id": "d", "label": "50" } ] }, { "id": "abstract-reasoning-s08-q02", "prompt": "A sequence runs: A, Z, B, Y, C, X. What comes next?", "choices": [ { "id": "a", "label": "W" }, { "id": "b", "label": "E" }, { "id": "c", "label": "D" }, { "id": "d", "label": "Y" } ] }, { "id": "abstract-reasoning-s08-q03", "prompt": "A sequence runs: ▲, A, ▲▲, B, ▲▲▲, C. What comes next?", "choices": [ { "id": "a", "label": "D" }, { "id": "b", "label": "▲▲▲▲" }, { "id": "c", "label": "▲▲▲" }, { "id": "d", "label": "▲▲▲▲▲" } ] }, { "id": "abstract-reasoning-s08-q04", "prompt": "A sequence runs: 2, 3, 4, 6, 6, 9, 8. What comes next?", "choices": [ { "id": "a", "label": "10" }, { "id": "b", "label": "9" }, { "id": "c", "label": "11" }, { "id": "d", "label": "12" } ] }, { "id": "abstract-reasoning-s08-q05", "prompt": "A sequence runs: Z, 1, X, 2, V, 4, T, 8. What comes next?", "choices": [ { "id": "a", "label": "S" }, { "id": "b", "label": "P" }, { "id": "c", "label": "R" }, { "id": "d", "label": "Q" } ] }, { "id": "abstract-reasoning-s08-q06", "prompt": "A sequence runs: ●, ■■, ●●●, ■■■■, ●●●●●. What comes next?", "choices": [ { "id": "a", "label": "■■■■■■" }, { "id": "b", "label": "●●●●●●" }, { "id": "c", "label": "■■■■■" }, { "id": "d", "label": "●●●●●●●" } ] }, { "id": "abstract-reasoning-s08-q07", "prompt": "A sequence runs: 1, 2, 4, 3, 9, 4, 16, 5. What comes next?", "choices": [ { "id": "a", "label": "20" }, { "id": "b", "label": "6" }, { "id": "c", "label": "36" }, { "id": "d", "label": "25" } ] }, { "id": "abstract-reasoning-s08-q08", "prompt": "A sequence of codes runs: A1, C3, E5, G7. What comes next?", "choices": [ { "id": "a", "label": "H8" }, { "id": "b", "label": "I9" }, { "id": "c", "label": "J9" }, { "id": "d", "label": "I8" } ] }, { "id": "abstract-reasoning-s08-q09", "prompt": "A sequence runs: 1, A, ●, 2, B, ●●, 3, C. What comes next?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "D" }, { "id": "c", "label": "●●" }, { "id": "d", "label": "●●●" } ] }, { "id": "abstract-reasoning-s08-q10", "prompt": "A sequence runs: 100, 1, 90, 2, 80, 4, 70, 8. What comes next?", "choices": [ { "id": "a", "label": "60" }, { "id": "b", "label": "16" }, { "id": "c", "label": "50" }, { "id": "d", "label": "10" } ] } ] }, { "id": "abstract-reasoning-s09", "title": "Rule induction: infer the hidden rule", "instructions": "A 'machine' transforms inputs into outputs: infer its hidden rule from the examples, then apply it.", "items": [ { "id": "abstract-reasoning-s09-q01", "prompt": "A machine transforms: 12 into 21, 47 into 74, and 58 into 85. What does it turn 39 into?", "choices": [ { "id": "a", "label": "40" }, { "id": "b", "label": "93" }, { "id": "c", "label": "36" }, { "id": "d", "label": "39" } ] }, { "id": "abstract-reasoning-s09-q02", "prompt": "A machine transforms: ABC into BCD, and HIJ into IJK. What does it turn PQR into?", "choices": [ { "id": "a", "label": "OPQ" }, { "id": "b", "label": "PQS" }, { "id": "c", "label": "RST" }, { "id": "d", "label": "QRS" } ] }, { "id": "abstract-reasoning-s09-q03", "prompt": "A machine transforms: 3 into 10, 5 into 16, and 7 into 22. What does it turn 9 into?", "choices": [ { "id": "a", "label": "28" }, { "id": "b", "label": "27" }, { "id": "c", "label": "30" }, { "id": "d", "label": "25" } ] }, { "id": "abstract-reasoning-s09-q04", "prompt": "A machine transforms: AB into ABB, and CD into CDD. What does it turn XY into?", "choices": [ { "id": "a", "label": "XXY" }, { "id": "b", "label": "XYXY" }, { "id": "c", "label": "XYY" }, { "id": "d", "label": "XY" } ] }, { "id": "abstract-reasoning-s09-q05", "prompt": "A machine transforms: 25 into 7, 63 into 9, and 48 into 12. What does it turn 57 into?", "choices": [ { "id": "a", "label": "12" }, { "id": "b", "label": "35" }, { "id": "c", "label": "13" }, { "id": "d", "label": "11" } ] }, { "id": "abstract-reasoning-s09-q06", "prompt": "A machine transforms: ●●●● into ●●, and ●●●●●● into ●●●. What does it turn ●●●●●●●● into?", "choices": [ { "id": "a", "label": "●●" }, { "id": "b", "label": "●●●●" }, { "id": "c", "label": "●●●●●" }, { "id": "d", "label": "●●●●●●" } ] }, { "id": "abstract-reasoning-s09-q07", "prompt": "A machine transforms: square into triangle, pentagon into square, and hexagon into pentagon. What does it turn a heptagon into?", "choices": [ { "id": "a", "label": "Octagon" }, { "id": "b", "label": "Pentagon" }, { "id": "c", "label": "Hexagon" }, { "id": "d", "label": "Heptagon" } ] }, { "id": "abstract-reasoning-s09-q08", "prompt": "A machine takes a pair of numbers: (2, 3) gives 8, (3, 4) gives 14, and (4, 5) gives 22. What does (5, 6) give?", "choices": [ { "id": "a", "label": "30" }, { "id": "b", "label": "28" }, { "id": "c", "label": "34" }, { "id": "d", "label": "32" } ] }, { "id": "abstract-reasoning-s09-q09", "prompt": "A machine transforms: A into 1, D into 4, and J into 10. What does it turn Q into?", "choices": [ { "id": "a", "label": "16" }, { "id": "b", "label": "18" }, { "id": "c", "label": "17" }, { "id": "d", "label": "15" } ] }, { "id": "abstract-reasoning-s09-q10", "prompt": "A machine answers YES to 121, 3443 and 78987, and NO to 123 and 3442. Which of these new inputs would it answer YES to?", "choices": [ { "id": "a", "label": "45653" }, { "id": "b", "label": "45664" }, { "id": "c", "label": "45674" }, { "id": "d", "label": "45654" } ] } ] }, { "id": "abstract-reasoning-s10", "title": "Combined and multi-step rules", "instructions": "These items chain several rules together. Track the intermediate result after every step.", "items": [ { "id": "abstract-reasoning-s10-q01", "prompt": "The operator R reverses a string; the operator D deletes its last symbol. Working from the inside out, what is D(R(58274))?", "choices": [ { "id": "a", "label": "8274" }, { "id": "b", "label": "5827" }, { "id": "c", "label": "4728" }, { "id": "d", "label": "47285" } ] }, { "id": "abstract-reasoning-s10-q02", "prompt": "A token sits at position 1 of a circle of eight positions numbered 1 to 8. Each step it moves forward three positions, wrapping past 8 back to 1. Where is it after five steps?", "choices": [ { "id": "a", "label": "Position 8" }, { "id": "b", "label": "Position 7" }, { "id": "c", "label": "Position 1" }, { "id": "d", "label": "Position 5" } ] }, { "id": "abstract-reasoning-s10-q03", "prompt": "A counter starts at 5. The rule alternates: first double, then subtract 3, then double, and so on. What is the counter after four steps?", "choices": [ { "id": "a", "label": "14" }, { "id": "b", "label": "17" }, { "id": "c", "label": "7" }, { "id": "d", "label": "11" } ] }, { "id": "abstract-reasoning-s10-q04", "prompt": "Apply two rules in order to the letters ACE: first shift every letter two places forward in the alphabet, then reverse the whole string. What results?", "choices": [ { "id": "a", "label": "CEG" }, { "id": "b", "label": "GEC" }, { "id": "c", "label": "ECA" }, { "id": "d", "label": "ACG" } ] }, { "id": "abstract-reasoning-s10-q05", "prompt": "A token starts white and flips colour (white to black or black to white) every time it passes a gate. It passes three gates of type P, which each flip it once, and two gates of type Q, which each flip it twice. What colour is it at the end?", "choices": [ { "id": "a", "label": "White" }, { "id": "b", "label": "It depends on the order of the gates" }, { "id": "c", "label": "It cannot be determined" }, { "id": "d", "label": "Black" } ] }, { "id": "abstract-reasoning-s10-q06", "prompt": "In each row of a 3×3 grid, the middle cell shows the left cell rotated 90° clockwise, and the right cell shows the middle cell rotated 90° clockwise again. Row 3's left cell is an arrow pointing left. Where does its right cell's arrow point?", "choices": [ { "id": "a", "label": "Up" }, { "id": "b", "label": "Right" }, { "id": "c", "label": "Down" }, { "id": "d", "label": "Left" } ] }, { "id": "abstract-reasoning-s10-q07", "prompt": "A sequence runs: 3, 4, 6, 10, 18. What comes next?", "choices": [ { "id": "a", "label": "34" }, { "id": "b", "label": "26" }, { "id": "c", "label": "30" }, { "id": "d", "label": "36" } ] }, { "id": "abstract-reasoning-s10-q08", "prompt": "A sequence runs: 2, 6, 12, 20, 30. What comes next?", "choices": [ { "id": "a", "label": "40" }, { "id": "b", "label": "36" }, { "id": "c", "label": "42" }, { "id": "d", "label": "44" } ] }, { "id": "abstract-reasoning-s10-q09", "prompt": "A code rule shifts every letter one place back in the alphabet and doubles every digit: C4F2 becomes B8E4. What does D3H5 become?", "choices": [ { "id": "a", "label": "C6G10" }, { "id": "b", "label": "E6I10" }, { "id": "c", "label": "C6G1" }, { "id": "d", "label": "D6H10" } ] }, { "id": "abstract-reasoning-s10-q10", "prompt": "The operator # doubles every symbol (#(AB) = AABB); the operator ∆ removes every second symbol (∆(ABCD) = AC). What is ∆(#(AB))?", "choices": [ { "id": "a", "label": "AABB" }, { "id": "b", "label": "AB" }, { "id": "c", "label": "BA" }, { "id": "d", "label": "An empty string" } ] } ] } ] }, "authoredHints": { "title": "Authored hints", "policy": "This cognitive practice source does not publish authored hints. Every item is listed as missing a hint, and no hint text is generated or inferred.", "items": [], "missingItemIds": [ "abstract-reasoning-s01-q01", "abstract-reasoning-s01-q02", "abstract-reasoning-s01-q03", "abstract-reasoning-s01-q04", "abstract-reasoning-s01-q05", "abstract-reasoning-s01-q06", "abstract-reasoning-s01-q07", "abstract-reasoning-s01-q08", "abstract-reasoning-s01-q09", "abstract-reasoning-s01-q10", "abstract-reasoning-s02-q01", "abstract-reasoning-s02-q02", "abstract-reasoning-s02-q03", "abstract-reasoning-s02-q04", "abstract-reasoning-s02-q05", "abstract-reasoning-s02-q06", "abstract-reasoning-s02-q07", "abstract-reasoning-s02-q08", "abstract-reasoning-s02-q09", "abstract-reasoning-s02-q10", "abstract-reasoning-s03-q01", "abstract-reasoning-s03-q02", "abstract-reasoning-s03-q03", "abstract-reasoning-s03-q04", "abstract-reasoning-s03-q05", "abstract-reasoning-s03-q06", "abstract-reasoning-s03-q07", "abstract-reasoning-s03-q08", "abstract-reasoning-s03-q09", "abstract-reasoning-s03-q10", "abstract-reasoning-s04-q01", "abstract-reasoning-s04-q02", "abstract-reasoning-s04-q03", "abstract-reasoning-s04-q04", "abstract-reasoning-s04-q05", "abstract-reasoning-s04-q06", "abstract-reasoning-s04-q07", "abstract-reasoning-s04-q08", "abstract-reasoning-s04-q09", "abstract-reasoning-s04-q10", "abstract-reasoning-s05-q01", "abstract-reasoning-s05-q02", "abstract-reasoning-s05-q03", "abstract-reasoning-s05-q04", "abstract-reasoning-s05-q05", "abstract-reasoning-s05-q06", "abstract-reasoning-s05-q07", "abstract-reasoning-s05-q08", "abstract-reasoning-s05-q09", "abstract-reasoning-s05-q10", "abstract-reasoning-s06-q01", "abstract-reasoning-s06-q02", "abstract-reasoning-s06-q03", "abstract-reasoning-s06-q04", "abstract-reasoning-s06-q05", "abstract-reasoning-s06-q06", "abstract-reasoning-s06-q07", "abstract-reasoning-s06-q08", "abstract-reasoning-s06-q09", "abstract-reasoning-s06-q10", "abstract-reasoning-s07-q01", "abstract-reasoning-s07-q02", "abstract-reasoning-s07-q03", "abstract-reasoning-s07-q04", "abstract-reasoning-s07-q05", "abstract-reasoning-s07-q06", "abstract-reasoning-s07-q07", "abstract-reasoning-s07-q08", "abstract-reasoning-s07-q09", "abstract-reasoning-s07-q10", "abstract-reasoning-s08-q01", "abstract-reasoning-s08-q02", "abstract-reasoning-s08-q03", "abstract-reasoning-s08-q04", "abstract-reasoning-s08-q05", "abstract-reasoning-s08-q06", "abstract-reasoning-s08-q07", "abstract-reasoning-s08-q08", "abstract-reasoning-s08-q09", "abstract-reasoning-s08-q10", "abstract-reasoning-s09-q01", "abstract-reasoning-s09-q02", "abstract-reasoning-s09-q03", "abstract-reasoning-s09-q04", "abstract-reasoning-s09-q05", "abstract-reasoning-s09-q06", "abstract-reasoning-s09-q07", "abstract-reasoning-s09-q08", "abstract-reasoning-s09-q09", "abstract-reasoning-s09-q10", "abstract-reasoning-s10-q01", "abstract-reasoning-s10-q02", "abstract-reasoning-s10-q03", "abstract-reasoning-s10-q04", "abstract-reasoning-s10-q05", "abstract-reasoning-s10-q06", "abstract-reasoning-s10-q07", "abstract-reasoning-s10-q08", "abstract-reasoning-s10-q09", "abstract-reasoning-s10-q10" ] }, "answerKey": { "title": "Answer key", "items": [ { "itemId": "abstract-reasoning-s01-q01", "correctChoiceId": "b", "correctChoiceLabel": "Square" }, { "itemId": "abstract-reasoning-s01-q02", "correctChoiceId": "c", "correctChoiceLabel": "Large" }, { "itemId": "abstract-reasoning-s01-q03", "correctChoiceId": "a", "correctChoiceLabel": "I" }, { "itemId": "abstract-reasoning-s01-q04", "correctChoiceId": "d", "correctChoiceLabel": "★★★★" }, { "itemId": "abstract-reasoning-s01-q05", "correctChoiceId": "b", "correctChoiceLabel": "Down" }, { "itemId": "abstract-reasoning-s01-q06", "correctChoiceId": "a", "correctChoiceLabel": "○" }, { "itemId": "abstract-reasoning-s01-q07", "correctChoiceId": "c", "correctChoiceLabel": "R" }, { "itemId": "abstract-reasoning-s01-q08", "correctChoiceId": "d", "correctChoiceLabel": "Sun" }, { "itemId": "abstract-reasoning-s01-q09", "correctChoiceId": "c", "correctChoiceLabel": "Hexagon" }, { "itemId": "abstract-reasoning-s01-q10", "correctChoiceId": "b", "correctChoiceLabel": "16 dots" }, { "itemId": "abstract-reasoning-s02-q01", "correctChoiceId": "d", "correctChoiceLabel": "Circle" }, { "itemId": "abstract-reasoning-s02-q02", "correctChoiceId": "a", "correctChoiceLabel": "S" }, { "itemId": "abstract-reasoning-s02-q03", "correctChoiceId": "c", "correctChoiceLabel": "F" }, { "itemId": "abstract-reasoning-s02-q04", "correctChoiceId": "b", "correctChoiceLabel": "Square" }, { "itemId": "abstract-reasoning-s02-q05", "correctChoiceId": "a", "correctChoiceLabel": "AB" }, { "itemId": "abstract-reasoning-s02-q06", "correctChoiceId": "d", "correctChoiceLabel": "4D" }, { "itemId": "abstract-reasoning-s02-q07", "correctChoiceId": "b", "correctChoiceLabel": "Hexagon" }, { "itemId": "abstract-reasoning-s02-q08", "correctChoiceId": "c", "correctChoiceLabel": "K" }, { "itemId": "abstract-reasoning-s02-q09", "correctChoiceId": "a", "correctChoiceLabel": "★★" }, { "itemId": "abstract-reasoning-s02-q10", "correctChoiceId": "c", "correctChoiceLabel": "E" }, { "itemId": "abstract-reasoning-s03-q01", "correctChoiceId": "c", "correctChoiceLabel": "Green square" }, { "itemId": "abstract-reasoning-s03-q02", "correctChoiceId": "b", "correctChoiceLabel": "Right" }, { "itemId": "abstract-reasoning-s03-q03", "correctChoiceId": "d", "correctChoiceLabel": "12" }, { "itemId": "abstract-reasoning-s03-q04", "correctChoiceId": "a", "correctChoiceLabel": "E" }, { "itemId": "abstract-reasoning-s03-q05", "correctChoiceId": "c", "correctChoiceLabel": "Black ▼" }, { "itemId": "abstract-reasoning-s03-q06", "correctChoiceId": "b", "correctChoiceLabel": "♥" }, { "itemId": "abstract-reasoning-s03-q07", "correctChoiceId": "a", "correctChoiceLabel": "3" }, { "itemId": "abstract-reasoning-s03-q08", "correctChoiceId": "d", "correctChoiceLabel": "■■■" }, { "itemId": "abstract-reasoning-s03-q09", "correctChoiceId": "d", "correctChoiceLabel": "Centre" }, { "itemId": "abstract-reasoning-s03-q10", "correctChoiceId": "b", "correctChoiceLabel": "y" }, { "itemId": "abstract-reasoning-s04-q01", "correctChoiceId": "a", "correctChoiceLabel": "9" }, { "itemId": "abstract-reasoning-s04-q02", "correctChoiceId": "d", "correctChoiceLabel": "2" }, { "itemId": "abstract-reasoning-s04-q03", "correctChoiceId": "b", "correctChoiceLabel": "16" }, { "itemId": "abstract-reasoning-s04-q04", "correctChoiceId": "c", "correctChoiceLabel": "32" }, { "itemId": "abstract-reasoning-s04-q05", "correctChoiceId": "d", "correctChoiceLabel": "4" }, { "itemId": "abstract-reasoning-s04-q06", "correctChoiceId": "a", "correctChoiceLabel": "17" }, { "itemId": "abstract-reasoning-s04-q07", "correctChoiceId": "c", "correctChoiceLabel": "25" }, { "itemId": "abstract-reasoning-s04-q08", "correctChoiceId": "b", "correctChoiceLabel": "15" }, { "itemId": "abstract-reasoning-s04-q09", "correctChoiceId": "d", "correctChoiceLabel": "8" }, { "itemId": "abstract-reasoning-s04-q10", "correctChoiceId": "a", "correctChoiceLabel": "13" }, { "itemId": "abstract-reasoning-s05-q01", "correctChoiceId": "b", "correctChoiceLabel": "Large square" }, { "itemId": "abstract-reasoning-s05-q02", "correctChoiceId": "a", "correctChoiceLabel": "q" }, { "itemId": "abstract-reasoning-s05-q03", "correctChoiceId": "d", "correctChoiceLabel": "Hexagon" }, { "itemId": "abstract-reasoning-s05-q04", "correctChoiceId": "c", "correctChoiceLabel": "White circle" }, { "itemId": "abstract-reasoning-s05-q05", "correctChoiceId": "b", "correctChoiceLabel": "DC" }, { "itemId": "abstract-reasoning-s05-q06", "correctChoiceId": "d", "correctChoiceLabel": "Cube" }, { "itemId": "abstract-reasoning-s05-q07", "correctChoiceId": "a", "correctChoiceLabel": "10" }, { "itemId": "abstract-reasoning-s05-q08", "correctChoiceId": "c", "correctChoiceLabel": "O" }, { "itemId": "abstract-reasoning-s05-q09", "correctChoiceId": "c", "correctChoiceLabel": "BAB" }, { "itemId": "abstract-reasoning-s05-q10", "correctChoiceId": "d", "correctChoiceLabel": "★■■" }, { "itemId": "abstract-reasoning-s06-q01", "correctChoiceId": "c", "correctChoiceLabel": "MLK" }, { "itemId": "abstract-reasoning-s06-q02", "correctChoiceId": "d", "correctChoiceLabel": "9582" }, { "itemId": "abstract-reasoning-s06-q03", "correctChoiceId": "a", "correctChoiceLabel": "XXYY" }, { "itemId": "abstract-reasoning-s06-q04", "correctChoiceId": "b", "correctChoiceLabel": "PRT" }, { "itemId": "abstract-reasoning-s06-q05", "correctChoiceId": "a", "correctChoiceLabel": "D, G, L" }, { "itemId": "abstract-reasoning-s06-q06", "correctChoiceId": "c", "correctChoiceLabel": "CCBBAA" }, { "itemId": "abstract-reasoning-s06-q07", "correctChoiceId": "d", "correctChoiceLabel": "YZWX" }, { "itemId": "abstract-reasoning-s06-q08", "correctChoiceId": "b", "correctChoiceLabel": "△" }, { "itemId": "abstract-reasoning-s06-q09", "correctChoiceId": "b", "correctChoiceLabel": "321" }, { "itemId": "abstract-reasoning-s06-q10", "correctChoiceId": "a", "correctChoiceLabel": "XYYX" }, { "itemId": "abstract-reasoning-s07-q01", "correctChoiceId": "d", "correctChoiceLabel": "Circle" }, { "itemId": "abstract-reasoning-s07-q02", "correctChoiceId": "b", "correctChoiceLabel": "5" }, { "itemId": "abstract-reasoning-s07-q03", "correctChoiceId": "c", "correctChoiceLabel": "Grey" }, { "itemId": "abstract-reasoning-s07-q04", "correctChoiceId": "a", "correctChoiceLabel": "A cross (both lines together)" }, { "itemId": "abstract-reasoning-s07-q05", "correctChoiceId": "d", "correctChoiceLabel": "Column 1" }, { "itemId": "abstract-reasoning-s07-q06", "correctChoiceId": "c", "correctChoiceLabel": "Heptagon" }, { "itemId": "abstract-reasoning-s07-q07", "correctChoiceId": "b", "correctChoiceLabel": "Up" }, { "itemId": "abstract-reasoning-s07-q08", "correctChoiceId": "a", "correctChoiceLabel": "9" }, { "itemId": "abstract-reasoning-s07-q09", "correctChoiceId": "b", "correctChoiceLabel": "A circle and a triangle" }, { "itemId": "abstract-reasoning-s07-q10", "correctChoiceId": "c", "correctChoiceLabel": "Medium" }, { "itemId": "abstract-reasoning-s08-q01", "correctChoiceId": "a", "correctChoiceLabel": "40" }, { "itemId": "abstract-reasoning-s08-q02", "correctChoiceId": "c", "correctChoiceLabel": "D" }, { "itemId": "abstract-reasoning-s08-q03", "correctChoiceId": "b", "correctChoiceLabel": "▲▲▲▲" }, { "itemId": "abstract-reasoning-s08-q04", "correctChoiceId": "d", "correctChoiceLabel": "12" }, { "itemId": "abstract-reasoning-s08-q05", "correctChoiceId": "c", "correctChoiceLabel": "R" }, { "itemId": "abstract-reasoning-s08-q06", "correctChoiceId": "a", "correctChoiceLabel": "■■■■■■" }, { "itemId": "abstract-reasoning-s08-q07", "correctChoiceId": "d", "correctChoiceLabel": "25" }, { "itemId": "abstract-reasoning-s08-q08", "correctChoiceId": "b", "correctChoiceLabel": "I9" }, { "itemId": "abstract-reasoning-s08-q09", "correctChoiceId": "d", "correctChoiceLabel": "●●●" }, { "itemId": "abstract-reasoning-s08-q10", "correctChoiceId": "a", "correctChoiceLabel": "60" }, { "itemId": "abstract-reasoning-s09-q01", "correctChoiceId": "b", "correctChoiceLabel": "93" }, { "itemId": "abstract-reasoning-s09-q02", "correctChoiceId": "d", "correctChoiceLabel": "QRS" }, { "itemId": "abstract-reasoning-s09-q03", "correctChoiceId": "a", "correctChoiceLabel": "28" }, { "itemId": "abstract-reasoning-s09-q04", "correctChoiceId": "c", "correctChoiceLabel": "XYY" }, { "itemId": "abstract-reasoning-s09-q05", "correctChoiceId": "a", "correctChoiceLabel": "12" }, { "itemId": "abstract-reasoning-s09-q06", "correctChoiceId": "b", "correctChoiceLabel": "●●●●" }, { "itemId": "abstract-reasoning-s09-q07", "correctChoiceId": "c", "correctChoiceLabel": "Hexagon" }, { "itemId": "abstract-reasoning-s09-q08", "correctChoiceId": "d", "correctChoiceLabel": "32" }, { "itemId": "abstract-reasoning-s09-q09", "correctChoiceId": "c", "correctChoiceLabel": "17" }, { "itemId": "abstract-reasoning-s09-q10", "correctChoiceId": "d", "correctChoiceLabel": "45654" }, { "itemId": "abstract-reasoning-s10-q01", "correctChoiceId": "c", "correctChoiceLabel": "4728" }, { "itemId": "abstract-reasoning-s10-q02", "correctChoiceId": "a", "correctChoiceLabel": "Position 8" }, { "itemId": "abstract-reasoning-s10-q03", "correctChoiceId": "d", "correctChoiceLabel": "11" }, { "itemId": "abstract-reasoning-s10-q04", "correctChoiceId": "b", "correctChoiceLabel": "GEC" }, { "itemId": "abstract-reasoning-s10-q05", "correctChoiceId": "d", "correctChoiceLabel": "Black" }, { "itemId": "abstract-reasoning-s10-q06", "correctChoiceId": "b", "correctChoiceLabel": "Right" }, { "itemId": "abstract-reasoning-s10-q07", "correctChoiceId": "a", "correctChoiceLabel": "34" }, { "itemId": "abstract-reasoning-s10-q08", "correctChoiceId": "c", "correctChoiceLabel": "42" }, { "itemId": "abstract-reasoning-s10-q09", "correctChoiceId": "a", "correctChoiceLabel": "C6G10" }, { "itemId": "abstract-reasoning-s10-q10", "correctChoiceId": "b", "correctChoiceLabel": "AB" } ] }, "workedExplanations": { "title": "Worked explanations", "items": [ { "itemId": "abstract-reasoning-s01-q01", "explanation": "The sequence simply alternates between two shapes, so after a circle the square returns." }, { "itemId": "abstract-reasoning-s01-q02", "explanation": "The three sizes cycle in a fixed order, so after medium the cycle continues with large." }, { "itemId": "abstract-reasoning-s01-q03", "explanation": "Each step skips exactly one letter of the alphabet, so G is followed by I." }, { "itemId": "abstract-reasoning-s01-q04", "explanation": "Each group adds one more star than the last, so three stars are followed by four." }, { "itemId": "abstract-reasoning-s01-q05", "explanation": "The arrow rotates a quarter turn clockwise each step through a four-direction cycle, so after right it points down." }, { "itemId": "abstract-reasoning-s01-q06", "explanation": "The repeating block is two black dots followed by one white dot, so the white dot is due next." }, { "itemId": "abstract-reasoning-s01-q07", "explanation": "Each step moves two letters backwards through the alphabet, so T is followed by R." }, { "itemId": "abstract-reasoning-s01-q08", "explanation": "The three symbols repeat in a fixed cycle, and the cycle has reached the sun's turn." }, { "itemId": "abstract-reasoning-s01-q09", "explanation": "The side count climbs 3, 4, 5, so the next shape has six sides, a hexagon." }, { "itemId": "abstract-reasoning-s01-q10", "explanation": "Each group has twice as many dots as the one before, so 8 doubles to 16." }, { "itemId": "abstract-reasoning-s02-q01", "explanation": "Three of the shapes are built entirely from straight sides; the circle is the only curved shape." }, { "itemId": "abstract-reasoning-s02-q02", "explanation": "X, K and T are drawn with straight strokes only, while S is drawn entirely with curves." }, { "itemId": "abstract-reasoning-s02-q03", "explanation": "A, H and M each have a vertical line of symmetry, their left and right halves mirror each other, but F does not." }, { "itemId": "abstract-reasoning-s02-q04", "explanation": "Cube, sphere and cylinder are solid three-dimensional forms; the square is a flat two-dimensional shape." }, { "itemId": "abstract-reasoning-s02-q05", "explanation": "Three of the pairs repeat the same letter twice; only one pairs two different letters." }, { "itemId": "abstract-reasoning-s02-q06", "explanation": "Three codes place a letter before its matching digit; one reverses the order and puts the digit first." }, { "itemId": "abstract-reasoning-s02-q07", "explanation": "The triangle, pentagon and heptagon have odd numbers of sides (3, 5, 7); the hexagon's six sides make it the only even one." }, { "itemId": "abstract-reasoning-s02-q08", "explanation": "B, D and H sit at alphabet positions 2, 4 and 8, each double the last, while K sits at position 11." }, { "itemId": "abstract-reasoning-s02-q09", "explanation": "Three groups contain exactly three identical symbols; the star group contains only two." }, { "itemId": "abstract-reasoning-s02-q10", "explanation": "S, N and Z look the same after a half-turn (180° rotation), but E does not share this rotational symmetry." }, { "itemId": "abstract-reasoning-s03-q01", "explanation": "Track each feature separately: the shape alternates, so a square is due; the colour cycle red-blue-green has reached green." }, { "itemId": "abstract-reasoning-s03-q02", "explanation": "The cycle is three directions long (up, right, down), and after up the cycle continues with right." }, { "itemId": "abstract-reasoning-s03-q03", "explanation": "Three hours past 9 wraps around the clock face back to 12, completing the four-step cycle." }, { "itemId": "abstract-reasoning-s03-q04", "explanation": "The sequence alternates between a fixed A and a letter that advances one step each visit (B, C, D), so E is due." }, { "itemId": "abstract-reasoning-s03-q05", "explanation": "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)." }, { "itemId": "abstract-reasoning-s03-q06", "explanation": "The cycle is four symbols long, so position 10 = two full cycles (8) plus 2 more, the second symbol of the cycle." }, { "itemId": "abstract-reasoning-s03-q07", "explanation": "Position 12 is exactly four complete cycles of three, so it lands on the final term of a cycle." }, { "itemId": "abstract-reasoning-s03-q08", "explanation": "The shapes alternate circle/square while the count rises by one each pair, so three squares follow three circles." }, { "itemId": "abstract-reasoning-s03-q09", "explanation": "The pendulum passes through the centre between every swing to a side, so centre always follows left or right." }, { "itemId": "abstract-reasoning-s03-q10", "explanation": "Run the two cycles separately: the letter cycle X-Y-Z has reached Y, and the case alternation has reached lower case." }, { "itemId": "abstract-reasoning-s04-q01", "explanation": "Each group adds two dots to the last, so 7 grows to 9." }, { "itemId": "abstract-reasoning-s04-q02", "explanation": "The pattern loses two blocks each step, so 4 shrinks to 2." }, { "itemId": "abstract-reasoning-s04-q03", "explanation": "The amount added grows by one each step (+1, +2, +3, +4), so the next step adds 5 to reach 16." }, { "itemId": "abstract-reasoning-s04-q04", "explanation": "Each count is twice the one before, so 16 doubles to 32." }, { "itemId": "abstract-reasoning-s04-q05", "explanation": "Each count is half the one before, so 8 halves to 4." }, { "itemId": "abstract-reasoning-s04-q06", "explanation": "Two rules alternate: double, then subtract one. After doubling 9 to 18, the next step subtracts one to give 17." }, { "itemId": "abstract-reasoning-s04-q07", "explanation": "The counts are square grids of side 1, 2, 3, 4, so the next grid is 5 × 5 = 25 dots." }, { "itemId": "abstract-reasoning-s04-q08", "explanation": "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." }, { "itemId": "abstract-reasoning-s04-q09", "explanation": "The rule alternates +3 then −2. After adding 3 to reach 10, the next step subtracts 2 to give 8." }, { "itemId": "abstract-reasoning-s04-q10", "explanation": "Adding the last two counts, 5 + 8, gives 13." }, { "itemId": "abstract-reasoning-s05-q01", "explanation": "The relationship enlarges the shape without changing it, so the square simply becomes large." }, { "itemId": "abstract-reasoning-s05-q02", "explanation": "b and d are left-right mirror images of each other, and the mirror image of p is q." }, { "itemId": "abstract-reasoning-s05-q03", "explanation": "The number names how many sides the shape has, and the six-sided shape is the hexagon." }, { "itemId": "abstract-reasoning-s05-q04", "explanation": "The relationship swaps the shading from black to white while keeping the shape the same." }, { "itemId": "abstract-reasoning-s05-q05", "explanation": "The relationship reverses the order of the two symbols, so CD becomes DC." }, { "itemId": "abstract-reasoning-s05-q06", "explanation": "The relationship turns a flat shape into its three-dimensional counterpart, and the solid built from squares is the cube." }, { "itemId": "abstract-reasoning-s05-q07", "explanation": "The relationship doubles the first number, and 5 doubled is 10." }, { "itemId": "abstract-reasoning-s05-q08", "explanation": "The relationship moves two places forward in the alphabet, and two letters after M comes O." }, { "itemId": "abstract-reasoning-s05-q09", "explanation": "The relationship swaps the roles of the two symbols: the outer symbol moves to the middle and vice versa." }, { "itemId": "abstract-reasoning-s05-q10", "explanation": "The relationship moves the last symbol to the front of the group, so the star leads the two squares." }, { "itemId": "abstract-reasoning-s06-q01", "explanation": "Reversing writes the symbols in the opposite order, so the last letter comes first." }, { "itemId": "abstract-reasoning-s06-q02", "explanation": "Only the outer symbols trade places, 2 and 9 swap, while the middle symbols 5 and 8 stay put." }, { "itemId": "abstract-reasoning-s06-q03", "explanation": "Each symbol is written twice in place before moving to the next, following the worked example exactly." }, { "itemId": "abstract-reasoning-s06-q04", "explanation": "The operator keeps the 1st, 3rd and 5th symbols and drops the 2nd and 4th, just as in the worked example." }, { "itemId": "abstract-reasoning-s06-q05", "explanation": "Each letter moves forward exactly one place: C to D, F to G, K to L." }, { "itemId": "abstract-reasoning-s06-q06", "explanation": "Work from the inside out: swapping first and last turns ABC into CBA, then doubling each symbol gives CCBBAA." }, { "itemId": "abstract-reasoning-s06-q07", "explanation": "Each rotation moves the front symbol to the back: WXYZ becomes XYZW, then XYZW becomes YZWX." }, { "itemId": "abstract-reasoning-s06-q08", "explanation": "Follow the cycle one step at a time: the circle first becomes a square, and the square then becomes a triangle." }, { "itemId": "abstract-reasoning-s06-q09", "explanation": "Reversing 1234 gives 4321, and removing the first symbol of that result leaves 321." }, { "itemId": "abstract-reasoning-s06-q10", "explanation": "The original string XY is followed by its reverse YX, producing a mirror-symmetric result." }, { "itemId": "abstract-reasoning-s07-q01", "explanation": "Each row must contain all three shapes exactly once, and the circle is the one still missing from row 3." }, { "itemId": "abstract-reasoning-s07-q02", "explanation": "Moving one cell to the right adds one dot, so the middle cell holds 4 + 1 = 5 dots." }, { "itemId": "abstract-reasoning-s07-q03", "explanation": "Each row shifts the previous row one place to the left, so row 3 continues white, black, grey, and grey also completes its column." }, { "itemId": "abstract-reasoning-s07-q04", "explanation": "Combining the two cells overlays their contents, and a vertical line laid over a horizontal line forms a cross." }, { "itemId": "abstract-reasoning-s07-q05", "explanation": "Columns 2 and 3 already have their single star, so row 3's star must occupy the only remaining column." }, { "itemId": "abstract-reasoning-s07-q06", "explanation": "The side count rises 5, 6 along the row, so the final cell holds the seven-sided heptagon." }, { "itemId": "abstract-reasoning-s07-q07", "explanation": "A quarter turn clockwise carries a left-pointing arrow round to point up." }, { "itemId": "abstract-reasoning-s07-q08", "explanation": "Applying the stated rule to the bottom-right cell gives 3 × 3 = 9 dots." }, { "itemId": "abstract-reasoning-s07-q09", "explanation": "The square appears in both cells so it is excluded, leaving the circle and triangle, which each appear only once." }, { "itemId": "abstract-reasoning-s07-q10", "explanation": "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." }, { "itemId": "abstract-reasoning-s08-q01", "explanation": "Two strands alternate: 1, 2, 3, 4 and 10, 20, 30. The next term belongs to the tens strand." }, { "itemId": "abstract-reasoning-s08-q02", "explanation": "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." }, { "itemId": "abstract-reasoning-s08-q03", "explanation": "Triangle groups (growing by one) alternate with advancing letters, and it is the triangles' turn with four." }, { "itemId": "abstract-reasoning-s08-q04", "explanation": "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." }, { "itemId": "abstract-reasoning-s08-q05", "explanation": "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." }, { "itemId": "abstract-reasoning-s08-q06", "explanation": "The shapes alternate circle/square while the count rises by one each term, so six squares follow five circles." }, { "itemId": "abstract-reasoning-s08-q07", "explanation": "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." }, { "itemId": "abstract-reasoning-s08-q08", "explanation": "The letters advance two places each step while the digits climb through the odd numbers, giving I paired with 9." }, { "itemId": "abstract-reasoning-s08-q09", "explanation": "Three strands rotate (a count, a letter, then a dot group that grows by one), and it is the dots' turn with three." }, { "itemId": "abstract-reasoning-s08-q10", "explanation": "One strand falls by ten (100, 90, 80, 70) while the other doubles (1, 2, 4, 8); the falling strand is due next." }, { "itemId": "abstract-reasoning-s09-q01", "explanation": "Each example reverses the order of the digits, so 39 becomes 93." }, { "itemId": "abstract-reasoning-s09-q02", "explanation": "The machine shifts every letter one place forward in the alphabet, so P, Q, R become Q, R, S." }, { "itemId": "abstract-reasoning-s09-q03", "explanation": "Each output is three times the input plus one, a rule all three examples satisfy, so 9 maps to 28." }, { "itemId": "abstract-reasoning-s09-q04", "explanation": "The machine repeats only the final symbol, so XY gains a second Y." }, { "itemId": "abstract-reasoning-s09-q05", "explanation": "Each output is the sum of the input's digits (2+5=7, 6+3=9, 4+8=12), so 5+7 gives 12." }, { "itemId": "abstract-reasoning-s09-q06", "explanation": "The machine halves the number of dots, so eight dots become four." }, { "itemId": "abstract-reasoning-s09-q07", "explanation": "Each example removes one side from the shape, so the seven-sided heptagon becomes a six-sided hexagon." }, { "itemId": "abstract-reasoning-s09-q08", "explanation": "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." }, { "itemId": "abstract-reasoning-s09-q09", "explanation": "Each output is the letter's position in the alphabet, and Q is the 17th letter." }, { "itemId": "abstract-reasoning-s09-q10", "explanation": "The machine accepts numbers that read the same forwards and backwards, and only 45654 is such a palindrome." }, { "itemId": "abstract-reasoning-s10-q01", "explanation": "Reversing 58274 gives 47285, and deleting that result's last symbol leaves 4728." }, { "itemId": "abstract-reasoning-s10-q02", "explanation": "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." }, { "itemId": "abstract-reasoning-s10-q03", "explanation": "Apply the alternating rules in order: 5 doubles to 10, minus 3 is 7, doubles to 14, minus 3 is 11." }, { "itemId": "abstract-reasoning-s10-q04", "explanation": "Shifting A, C, E forward two places gives C, E, G; reversing that intermediate result gives G, E, C." }, { "itemId": "abstract-reasoning-s10-q05", "explanation": "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." }, { "itemId": "abstract-reasoning-s10-q06", "explanation": "Two quarter turns clockwise make a half turn, and a half turn points a left-facing arrow to the right." }, { "itemId": "abstract-reasoning-s10-q07", "explanation": "The gaps between terms double each step (+1, +2, +4, +8), so the next gap is +16, giving 34." }, { "itemId": "abstract-reasoning-s10-q08", "explanation": "The gaps grow by two each step (+4, +6, +8, +10), so the next gap is +12, giving 42." }, { "itemId": "abstract-reasoning-s10-q09", "explanation": "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." }, { "itemId": "abstract-reasoning-s10-q10", "explanation": "Doubling AB gives AABB, and keeping the 1st and 3rd symbols of that result restores the original AB, the two operators undo each other." } ] } }