{ "format": "novus-learn-open-practice", "version": 1, "packId": "cognitive-skills-diagrammatic-reasoning", "source": "cognitive-skills", "slug": "diagrammatic-reasoning", "title": "Diagrammatic reasoning: transformations, flows, and rule diagrams: open practice pack", "subtitle": "100 untimed questions across 10 authored sections.", "sourceHref": "/cognitive-skills/diagrammatic-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": [ "One hundred untimed self-check items across ten sections, moving from single-box flows to integrated multi-stage systems. Every diagram is described in words and every rule you need appears in the prompt. No outside knowledge required.", "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": "diagrammatic-reasoning-s01", "title": "Reading single-step flow diagrams", "instructions": "Each item describes one operation box. Apply its rule exactly as stated.", "items": [ { "id": "diagrammatic-reasoning-s01-q01", "prompt": "A flow diagram shows a single box labelled 'Add 4'. The number 9 enters the box. What number comes out?", "choices": [ { "id": "a", "label": "5" }, { "id": "b", "label": "12" }, { "id": "c", "label": "13" }, { "id": "d", "label": "36" } ] }, { "id": "diagrammatic-reasoning-s01-q02", "prompt": "A box labelled 'Double' receives the number 7. What is the output?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "14" }, { "id": "c", "label": "21" }, { "id": "d", "label": "49" } ] }, { "id": "diagrammatic-reasoning-s01-q03", "prompt": "A box labelled 'Reverse' receives the letter sequence P-Q-R. What sequence comes out?", "choices": [ { "id": "a", "label": "P-Q-R" }, { "id": "b", "label": "Q-P-R" }, { "id": "c", "label": "R-Q-P" }, { "id": "d", "label": "R-P-Q" } ] }, { "id": "diagrammatic-reasoning-s01-q04", "prompt": "A box labelled 'Remove the last item' receives the list: apple, pear, plum. What list comes out?", "choices": [ { "id": "a", "label": "apple, pear" }, { "id": "b", "label": "pear, plum" }, { "id": "c", "label": "apple, plum" }, { "id": "d", "label": "apple, pear, plum" } ] }, { "id": "diagrammatic-reasoning-s01-q05", "prompt": "A box labelled 'Rotate 90° clockwise' receives a printed arrow pointing straight up. Which way does the arrow point on the way out?", "choices": [ { "id": "a", "label": "Up" }, { "id": "b", "label": "Down" }, { "id": "c", "label": "Left" }, { "id": "d", "label": "Right" } ] }, { "id": "diagrammatic-reasoning-s01-q06", "prompt": "A box labelled 'Swap the first and last symbols' receives the sequence ★ ● ▲ ■. What comes out?", "choices": [ { "id": "a", "label": "■ ● ▲ ★" }, { "id": "b", "label": "● ★ ■ ▲" }, { "id": "c", "label": "■ ▲ ● ★" }, { "id": "d", "label": "★ ■ ▲ ●" } ] }, { "id": "diagrammatic-reasoning-s01-q07", "prompt": "A box labelled 'Halve' receives the number 26. What is the output?", "choices": [ { "id": "a", "label": "12" }, { "id": "b", "label": "13" }, { "id": "c", "label": "24" }, { "id": "d", "label": "52" } ] }, { "id": "diagrammatic-reasoning-s01-q08", "prompt": "A box labelled 'Toggle shading' turns white figures black and black figures white without changing the shape. A white triangle enters. What comes out?", "choices": [ { "id": "a", "label": "A white triangle" }, { "id": "b", "label": "A black square" }, { "id": "c", "label": "A white circle" }, { "id": "d", "label": "A black triangle" } ] }, { "id": "diagrammatic-reasoning-s01-q09", "prompt": "A box labelled 'Repeat the whole sequence twice' receives the sequence A-B. What comes out?", "choices": [ { "id": "a", "label": "A-A-B-B" }, { "id": "b", "label": "A-B-A-B" }, { "id": "c", "label": "A-B-B-A" }, { "id": "d", "label": "B-A-B-A" } ] }, { "id": "diagrammatic-reasoning-s01-q10", "prompt": "A box labelled 'Subtract 6' receives the number 6. What is the output?", "choices": [ { "id": "a", "label": "0" }, { "id": "b", "label": "1" }, { "id": "c", "label": "6" }, { "id": "d", "label": "12" } ] } ] }, { "id": "diagrammatic-reasoning-s02", "title": "Two-step operator chains", "instructions": "Apply the two boxes strictly in the order shown, left to right.", "items": [ { "id": "diagrammatic-reasoning-s02-q01", "prompt": "The number 5 enters [Add 3] and the result enters [Double]. What is the output?", "choices": [ { "id": "a", "label": "13" }, { "id": "b", "label": "16" }, { "id": "c", "label": "11" }, { "id": "d", "label": "10" } ] }, { "id": "diagrammatic-reasoning-s02-q02", "prompt": "The number 12 enters [Halve] and the result enters [Subtract 2]. What is the output?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "5" }, { "id": "c", "label": "8" }, { "id": "d", "label": "10" } ] }, { "id": "diagrammatic-reasoning-s02-q03", "prompt": "The letters C-A-T enter [Reverse] and the result enters [Remove the last letter]. What comes out?", "choices": [ { "id": "a", "label": "A-T" }, { "id": "b", "label": "C-A" }, { "id": "c", "label": "T-C" }, { "id": "d", "label": "T-A" } ] }, { "id": "diagrammatic-reasoning-s02-q04", "prompt": "An arrow pointing north enters [Rotate 90° clockwise] and the result enters [Rotate 180°]. Which way does it finally point?", "choices": [ { "id": "a", "label": "North" }, { "id": "b", "label": "East" }, { "id": "c", "label": "West" }, { "id": "d", "label": "South" } ] }, { "id": "diagrammatic-reasoning-s02-q05", "prompt": "The list 2, 4, 6, 8 enters [Remove the first item] and the result enters [Reverse]. What comes out?", "choices": [ { "id": "a", "label": "8, 6, 4, 2" }, { "id": "b", "label": "8, 6, 4" }, { "id": "c", "label": "4, 6, 8" }, { "id": "d", "label": "6, 4, 2" } ] }, { "id": "diagrammatic-reasoning-s02-q06", "prompt": "The number 3 enters [Square] and the result enters [Add 1]. What is the output?", "choices": [ { "id": "a", "label": "16" }, { "id": "b", "label": "7" }, { "id": "c", "label": "9" }, { "id": "d", "label": "10" } ] }, { "id": "diagrammatic-reasoning-s02-q07", "prompt": "A white circle enters [Toggle shading] and the result enters [Rotate 90° clockwise]. What comes out?", "choices": [ { "id": "a", "label": "A black circle" }, { "id": "b", "label": "A white circle" }, { "id": "c", "label": "A black square" }, { "id": "d", "label": "A white square" } ] }, { "id": "diagrammatic-reasoning-s02-q08", "prompt": "The word STAR enters [Swap the first and last letters] and the result enters [Reverse]. What comes out?", "choices": [ { "id": "a", "label": "RATS" }, { "id": "b", "label": "RTAS" }, { "id": "c", "label": "SATR" }, { "id": "d", "label": "TARS" } ] }, { "id": "diagrammatic-reasoning-s02-q09", "prompt": "The number 18 enters [Subtract 4] and the result enters [Halve]. What is the output?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "5" }, { "id": "c", "label": "7" }, { "id": "d", "label": "14" } ] }, { "id": "diagrammatic-reasoning-s02-q10", "prompt": "The number 6 enters [Add 2] then [Double], giving 16. If the same two boxes are wired in the opposite order, [Double] then [Add 2], what output does 6 produce?", "choices": [ { "id": "a", "label": "16" }, { "id": "b", "label": "14" }, { "id": "c", "label": "12" }, { "id": "d", "label": "10" } ] } ] }, { "id": "diagrammatic-reasoning-s03", "title": "Inferring hidden rules from examples", "instructions": "Each box's rule is unknown: deduce it from the example pairs by testing every candidate against every pair.", "items": [ { "id": "diagrammatic-reasoning-s03-q01", "prompt": "A mystery box turns 3 into 6, 5 into 10, and 9 into 18. What is the box's rule?", "choices": [ { "id": "a", "label": "It adds 3" }, { "id": "b", "label": "It doubles" }, { "id": "c", "label": "It squares" }, { "id": "d", "label": "It adds 5" } ] }, { "id": "diagrammatic-reasoning-s03-q02", "prompt": "A mystery box turns 10 into 7, 8 into 5, and 6 into 3. What is its rule?", "choices": [ { "id": "a", "label": "It halves" }, { "id": "b", "label": "It subtracts 2" }, { "id": "c", "label": "It subtracts 4" }, { "id": "d", "label": "It subtracts 3" } ] }, { "id": "diagrammatic-reasoning-s03-q03", "prompt": "A mystery box turns CAT into TAC and STOP into POTS. What is its rule?", "choices": [ { "id": "a", "label": "It reverses all the letters" }, { "id": "b", "label": "It swaps only the first and last letters" }, { "id": "c", "label": "It moves the last letter to the front" }, { "id": "d", "label": "It writes the letters in alphabetical order" } ] }, { "id": "diagrammatic-reasoning-s03-q04", "prompt": "A mystery box turns 4 into 16, 5 into 25, and 7 into 49. What is its rule?", "choices": [ { "id": "a", "label": "It multiplies by 4" }, { "id": "b", "label": "It adds 12" }, { "id": "c", "label": "It squares" }, { "id": "d", "label": "It multiplies by 5" } ] }, { "id": "diagrammatic-reasoning-s03-q05", "prompt": "A mystery box turns the sequence 1-2-3 into 1-2-3-1, and the sequence X-Y into X-Y-X. What is its rule?", "choices": [ { "id": "a", "label": "It repeats the whole sequence" }, { "id": "b", "label": "It copies the first symbol onto the end" }, { "id": "c", "label": "It copies the last symbol onto the front" }, { "id": "d", "label": "It reverses the sequence" } ] }, { "id": "diagrammatic-reasoning-s03-q06", "prompt": "A mystery box turns 7 into 15, 10 into 21, and 4 into 9. What is its rule?", "choices": [ { "id": "a", "label": "It doubles, then adds 1" }, { "id": "b", "label": "It adds 8" }, { "id": "c", "label": "It doubles, then subtracts 1" }, { "id": "d", "label": "It triples, then subtracts 6" } ] }, { "id": "diagrammatic-reasoning-s03-q07", "prompt": "A mystery box turns a black square into a white square, and a white triangle into a black triangle. What is its rule?", "choices": [ { "id": "a", "label": "It turns every figure black" }, { "id": "b", "label": "It turns every figure white" }, { "id": "c", "label": "It changes the shape but keeps the shading" }, { "id": "d", "label": "It swaps the shading but keeps the shape" } ] }, { "id": "diagrammatic-reasoning-s03-q08", "prompt": "A mystery box turns 12 into 6, 20 into 10, and 8 into 4. What is its rule?", "choices": [ { "id": "a", "label": "It subtracts 6" }, { "id": "b", "label": "It subtracts 10" }, { "id": "c", "label": "It halves" }, { "id": "d", "label": "It divides by 3" } ] }, { "id": "diagrammatic-reasoning-s03-q09", "prompt": "A mystery box turns BOLT into BOL, RAIN into RAI, and TREE into TRE. What is its rule?", "choices": [ { "id": "a", "label": "It removes the last letter" }, { "id": "b", "label": "It removes the first letter" }, { "id": "c", "label": "It keeps only the first letter" }, { "id": "d", "label": "It removes all vowels" } ] }, { "id": "diagrammatic-reasoning-s03-q10", "prompt": "A mystery box turns 2 into 8. Which rule is consistent with BOTH 2→8 and 3→27?", "choices": [ { "id": "a", "label": "It multiplies by 4" }, { "id": "b", "label": "It cubes" }, { "id": "c", "label": "It adds 6" }, { "id": "d", "label": "It squares, then adds 4" } ] } ] }, { "id": "diagrammatic-reasoning-s04", "title": "Sequence and series patterns", "instructions": "Work out the pattern that generates each series, then predict the next term.", "items": [ { "id": "diagrammatic-reasoning-s04-q01", "prompt": "A series of frames shows: 1 dot, 2 dots, 3 dots, 4 dots. How many dots are in the next frame?", "choices": [ { "id": "a", "label": "4 dots" }, { "id": "b", "label": "6 dots" }, { "id": "c", "label": "3 dots" }, { "id": "d", "label": "5 dots" } ] }, { "id": "diagrammatic-reasoning-s04-q02", "prompt": "A series of squares alternates: black, white, black, white. What colour is the next square?", "choices": [ { "id": "a", "label": "Black" }, { "id": "b", "label": "White" }, { "id": "c", "label": "Grey" }, { "id": "d", "label": "Striped" } ] }, { "id": "diagrammatic-reasoning-s04-q03", "prompt": "An arrow rotates the same amount each frame: it points up, then right, then down. Where does it point next?", "choices": [ { "id": "a", "label": "Up" }, { "id": "b", "label": "Right" }, { "id": "c", "label": "Left" }, { "id": "d", "label": "Down" } ] }, { "id": "diagrammatic-reasoning-s04-q04", "prompt": "A series of frames shows: 1 black dot, then 2 white dots, then 3 black dots, then 4 white dots. What does the next frame show?", "choices": [ { "id": "a", "label": "5 white dots" }, { "id": "b", "label": "5 black dots" }, { "id": "c", "label": "4 black dots" }, { "id": "d", "label": "6 white dots" } ] }, { "id": "diagrammatic-reasoning-s04-q05", "prompt": "A series of shapes shows: triangle, square, pentagon. Which shape comes next?", "choices": [ { "id": "a", "label": "Circle" }, { "id": "b", "label": "Triangle" }, { "id": "c", "label": "Octagon" }, { "id": "d", "label": "Hexagon" } ] }, { "id": "diagrammatic-reasoning-s04-q06", "prompt": "A star sits in the top-left corner of a square frame, then the top-right corner, then the bottom-right corner. Where is it in the next frame?", "choices": [ { "id": "a", "label": "Top-left corner" }, { "id": "b", "label": "Bottom-left corner" }, { "id": "c", "label": "Top-right corner" }, { "id": "d", "label": "The centre" } ] }, { "id": "diagrammatic-reasoning-s04-q07", "prompt": "What is the next number in the series: 2, 4, 3, 6, 5, 10, 9, ...?", "choices": [ { "id": "a", "label": "18" }, { "id": "b", "label": "11" }, { "id": "c", "label": "8" }, { "id": "d", "label": "13" } ] }, { "id": "diagrammatic-reasoning-s04-q08", "prompt": "What is the next letter in the series: A, C, F, J, ...?", "choices": [ { "id": "a", "label": "N" }, { "id": "b", "label": "M" }, { "id": "c", "label": "O" }, { "id": "d", "label": "P" } ] }, { "id": "diagrammatic-reasoning-s04-q09", "prompt": "A series shows: a small arrow pointing up, a medium arrow pointing right, a large arrow pointing down. Sizes cycle small → medium → large → small, and the arrow keeps rotating 90° clockwise. What comes next?", "choices": [ { "id": "a", "label": "A large arrow pointing left" }, { "id": "b", "label": "A medium arrow pointing left" }, { "id": "c", "label": "A small arrow pointing up" }, { "id": "d", "label": "A small arrow pointing left" } ] }, { "id": "diagrammatic-reasoning-s04-q10", "prompt": "A 3×3 grid of dot counts reads: row 1: 1, 2, 3; row 2: 2, 3, 4; row 3: 3, 4, ?. What number completes the grid?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "6" }, { "id": "c", "label": "5" }, { "id": "d", "label": "7" } ] } ] }, { "id": "diagrammatic-reasoning-s05", "title": "Branching flowcharts and decisions", "instructions": "Follow each decision diamond carefully. Answer the question asked at each branch before moving on.", "items": [ { "id": "diagrammatic-reasoning-s05-q01", "prompt": "A flowchart takes the number 7 to a decision: 'Is it even?' Yes leads to [Add 1]; No leads to [Add 3]. What is the output?", "choices": [ { "id": "a", "label": "8" }, { "id": "b", "label": "7" }, { "id": "c", "label": "10" }, { "id": "d", "label": "11" } ] }, { "id": "diagrammatic-reasoning-s05-q02", "prompt": "A flowchart takes the number 12 to a decision: 'Is it greater than 10?' Yes leads to [Halve]; No leads to [Double]. What is the output?", "choices": [ { "id": "a", "label": "6" }, { "id": "b", "label": "24" }, { "id": "c", "label": "12" }, { "id": "d", "label": "5" } ] }, { "id": "diagrammatic-reasoning-s05-q03", "prompt": "A flowchart takes the number 9 through two decisions. First: 'Is it even?' Yes → [Halve]; No → [Add 1]. Then: 'Is the result greater than 8?' Yes → [Subtract 5]; No → [Add 5]. What is the output?", "choices": [ { "id": "a", "label": "15" }, { "id": "b", "label": "5" }, { "id": "c", "label": "10" }, { "id": "d", "label": "4" } ] }, { "id": "diagrammatic-reasoning-s05-q04", "prompt": "A flowchart takes the word ORANGE through two decisions. First: 'Does it have more than 5 letters?' Yes → [Remove the last letter]. Then: 'Does it start with a vowel?' Yes → [Reverse it]. What comes out?", "choices": [ { "id": "a", "label": "ORANG" }, { "id": "b", "label": "EGNARO" }, { "id": "c", "label": "ORANGE" }, { "id": "d", "label": "GNARO" } ] }, { "id": "diagrammatic-reasoning-s05-q05", "prompt": "A flowchart takes the number 15 through two decisions. First: 'Is it a multiple of 3?' Yes → [Divide by 3]; No → [Add 3]. Then: 'Is the result odd?' Yes → [Add 1]; No → [Halve]. What is the output?", "choices": [ { "id": "a", "label": "6" }, { "id": "b", "label": "5" }, { "id": "c", "label": "18" }, { "id": "d", "label": "9" } ] }, { "id": "diagrammatic-reasoning-s05-q06", "prompt": "A parcel-sorting flowchart asks in order: 'Does it weigh over 2 kg?' Yes → send to Depot B. No → 'Is it marked fragile?' Yes → send to Depot C; No → send to Depot A. Where does a 1.5 kg parcel marked fragile go?", "choices": [ { "id": "a", "label": "Depot A" }, { "id": "b", "label": "Depot B" }, { "id": "c", "label": "Depot C" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "diagrammatic-reasoning-s05-q07", "prompt": "Using the same sorting chart, over 2 kg → Depot B; otherwise fragile → Depot C; otherwise → Depot A, which parcel ends up at Depot A?", "choices": [ { "id": "a", "label": "A 3 kg parcel, not fragile" }, { "id": "b", "label": "A 1 kg parcel, marked fragile" }, { "id": "c", "label": "A 2.5 kg parcel, marked fragile" }, { "id": "d", "label": "A 1.8 kg parcel, not fragile" } ] }, { "id": "diagrammatic-reasoning-s05-q08", "prompt": "A flowchart takes 24 through three decisions in order: 'Even?' Yes → [Halve]. 'Multiple of 3?' Yes → [Divide by 3]. 'Greater than 5?' No → [Add 10]. What is the output?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "14" }, { "id": "c", "label": "12" }, { "id": "d", "label": "24" } ] }, { "id": "diagrammatic-reasoning-s05-q09", "prompt": "A flowchart doubles even inputs and adds 5 to odd inputs. The output was 18. What was the input?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "13" }, { "id": "c", "label": "36" }, { "id": "d", "label": "23" } ] }, { "id": "diagrammatic-reasoning-s05-q10", "prompt": "A flowchart takes the pair (6, 9). First decision: 'Is the first number even?' Yes → [Swap the pair]. Second decision: 'Is the sum greater than 14?' Yes → output the sum; No → output the difference. What is the output?", "choices": [ { "id": "a", "label": "3" }, { "id": "b", "label": "6" }, { "id": "c", "label": "9" }, { "id": "d", "label": "15" } ] } ] }, { "id": "diagrammatic-reasoning-s06", "title": "State and process diagrams", "instructions": "Track the current state after each signal. States change only when a listed transition allows it.", "items": [ { "id": "diagrammatic-reasoning-s06-q01", "prompt": "A traffic system cycles Green → Amber → Red → Green, one step per change. It currently shows Amber. What does it show after two changes?", "choices": [ { "id": "a", "label": "Green" }, { "id": "b", "label": "Red" }, { "id": "c", "label": "Amber" }, { "id": "d", "label": "Flashing amber" } ] }, { "id": "diagrammatic-reasoning-s06-q02", "prompt": "A door has states Locked, Closed, and Open. 'Turn key' switches between Locked and Closed. 'Push' moves Closed to Open and has no effect otherwise. Starting from Locked, apply: turn key, push. What state results?", "choices": [ { "id": "a", "label": "Locked" }, { "id": "b", "label": "Closed" }, { "id": "c", "label": "Open" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "diagrammatic-reasoning-s06-q03", "prompt": "A ticket machine moves Idle → (insert coin) → Ready → (press button) → Printing → (finishes automatically) → Idle. From Idle, a coin is inserted and the button is pressed. What state is the machine in?", "choices": [ { "id": "a", "label": "Idle" }, { "id": "b", "label": "Ready" }, { "id": "c", "label": "Refunding" }, { "id": "d", "label": "Printing" } ] }, { "id": "diagrammatic-reasoning-s06-q04", "prompt": "The same ticket machine ignores a button press while Idle. From Idle, the sequence is: press button, insert coin, press button. What state results?", "choices": [ { "id": "a", "label": "Idle" }, { "id": "b", "label": "Printing" }, { "id": "c", "label": "Ready" }, { "id": "d", "label": "The machine jams" } ] }, { "id": "diagrammatic-reasoning-s06-q05", "prompt": "A lift starts at floor 2. Each U signal moves it up one floor and each D signal moves it down one. After the signals U, U, D, U, which floor is it on?", "choices": [ { "id": "a", "label": "Floor 3" }, { "id": "b", "label": "Floor 5" }, { "id": "c", "label": "Floor 4" }, { "id": "d", "label": "Floor 2" } ] }, { "id": "diagrammatic-reasoning-s06-q06", "prompt": "A washing machine runs Fill → Wash → Rinse → Spin → Done. An 'advance' signal moves it one stage on; a 'hold' signal keeps the current stage. From Fill, the signals are: advance, advance, hold, advance. What stage is it in?", "choices": [ { "id": "a", "label": "Spin" }, { "id": "b", "label": "Rinse" }, { "id": "c", "label": "Wash" }, { "id": "d", "label": "Done" } ] }, { "id": "diagrammatic-reasoning-s06-q07", "prompt": "A turnstile has two states. In Locked, a coin unlocks it and a push does nothing. In Unlocked, a push locks it again and a coin does nothing. From Locked, apply: coin, coin, push, push. What state results?", "choices": [ { "id": "a", "label": "Unlocked" }, { "id": "b", "label": "Locked" }, { "id": "c", "label": "Jammed" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "diagrammatic-reasoning-s06-q08", "prompt": "In a conveyor network, Station 1 sends even-numbered crates to Station 3 and odd-numbered crates to Station 2. Which stations does crate number 8 visit?", "choices": [ { "id": "a", "label": "Stations 1 and 2" }, { "id": "b", "label": "Station 2 only" }, { "id": "c", "label": "Stations 1, 2 and 3" }, { "id": "d", "label": "Stations 1 and 3" } ] }, { "id": "diagrammatic-reasoning-s06-q09", "prompt": "A worker's status moves down one level (Fresh → Tired → Exhausted) after every second task completed at the current level. A rest moves the status up one level and resets the task count. Starting Fresh, the sequence is: task, task, task, rest, task. What is the final status?", "choices": [ { "id": "a", "label": "Fresh" }, { "id": "b", "label": "Tired" }, { "id": "c", "label": "Exhausted" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "diagrammatic-reasoning-s06-q10", "prompt": "A vending machine charges 30p. Credit accumulates as coins are inserted; the moment credit reaches 30p or more it vends and keeps only the excess as credit. Coins inserted: 20p, 20p, 10p. What is the final credit?", "choices": [ { "id": "a", "label": "0p" }, { "id": "b", "label": "10p" }, { "id": "c", "label": "20p" }, { "id": "d", "label": "30p" } ] } ] }, { "id": "diagrammatic-reasoning-s07", "title": "Deducing unknown operators in pipelines", "instructions": "Work out what each mystery operator does from its examples before applying it to the new input.", "items": [ { "id": "diagrammatic-reasoning-s07-q01", "prompt": "Operator ◆ turns 4 into 8 and 10 into 20. What does ◆ give for the input 6?", "choices": [ { "id": "a", "label": "10" }, { "id": "b", "label": "12" }, { "id": "c", "label": "8" }, { "id": "d", "label": "36" } ] }, { "id": "diagrammatic-reasoning-s07-q02", "prompt": "Operator ● turns A-B-C into C-B-A and P-Q into Q-P. What does ● give for R-S-T?", "choices": [ { "id": "a", "label": "R-S-T" }, { "id": "b", "label": "S-R-T" }, { "id": "c", "label": "R-T-S" }, { "id": "d", "label": "T-S-R" } ] }, { "id": "diagrammatic-reasoning-s07-q03", "prompt": "Operator ◆ doubles its input. Operator ● turns 5 into 8 and 9 into 12. What is the output of 4 → [◆] → [●]?", "choices": [ { "id": "a", "label": "11" }, { "id": "b", "label": "14" }, { "id": "c", "label": "10" }, { "id": "d", "label": "19" } ] }, { "id": "diagrammatic-reasoning-s07-q04", "prompt": "Operator ▲ turns 1-2-3 into 2-3, and 7-8-9-10 into 8-9-10. What does ▲ give for X-Y-Z?", "choices": [ { "id": "a", "label": "X-Y" }, { "id": "b", "label": "Z" }, { "id": "c", "label": "Y-Z" }, { "id": "d", "label": "X-Z" } ] }, { "id": "diagrammatic-reasoning-s07-q05", "prompt": "A single mystery box turns 3 into 9 and 5 into 15. What is its rule?", "choices": [ { "id": "a", "label": "It squares" }, { "id": "b", "label": "It adds 6" }, { "id": "c", "label": "It multiplies by 3" }, { "id": "d", "label": "It adds 10" } ] }, { "id": "diagrammatic-reasoning-s07-q06", "prompt": "In the pipeline input → [P] → [Q] → output, the input 2 produces 9 and the input 5 produces 15. P doubles its input. What must Q do?", "choices": [ { "id": "a", "label": "Add 3" }, { "id": "b", "label": "Double" }, { "id": "c", "label": "Subtract 5" }, { "id": "d", "label": "Add 5" } ] }, { "id": "diagrammatic-reasoning-s07-q07", "prompt": "Operator ■ toggles shading (white ↔ black). Operator ▲ rotates a figure 90° clockwise. A white arrow pointing up passes through [▲] then [■]. What comes out?", "choices": [ { "id": "a", "label": "A white arrow pointing right" }, { "id": "b", "label": "A black arrow pointing right" }, { "id": "c", "label": "A black arrow pointing up" }, { "id": "d", "label": "A black arrow pointing left" } ] }, { "id": "diagrammatic-reasoning-s07-q08", "prompt": "Two boxes, [Add 2] and [Halve], are wired one after the other in an unknown order. The input 6 produces the output 5. Which order are they in?", "choices": [ { "id": "a", "label": "Halve first, then Add 2" }, { "id": "b", "label": "Add 2 first, then Halve" }, { "id": "c", "label": "Either order gives 5" }, { "id": "d", "label": "Neither order can give 5" } ] }, { "id": "diagrammatic-reasoning-s07-q09", "prompt": "In the pipeline input → [Reverse] → [◇] → output, the input 4-7-2 produces 2-7 and the input 1-5 produces 5. What does ◇ do?", "choices": [ { "id": "a", "label": "It removes the first item" }, { "id": "b", "label": "It keeps only the first item" }, { "id": "c", "label": "It reverses again" }, { "id": "d", "label": "It removes the last item" } ] }, { "id": "diagrammatic-reasoning-s07-q10", "prompt": "In the pipeline 5 → [Double] → [X] → [Double] → 14, operator X applies the same rule every time. What does X give for the input 12?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "15" }, { "id": "c", "label": "24" }, { "id": "d", "label": "6" } ] } ] }, { "id": "diagrammatic-reasoning-s08", "title": "Loops and repeated processes", "instructions": "Repeat the rule exactly as stated and re-check the stopping condition after every pass.", "items": [ { "id": "diagrammatic-reasoning-s08-q01", "prompt": "Start with 3. Keep doubling until the number exceeds 20, then stop. What is the final number?", "choices": [ { "id": "a", "label": "12" }, { "id": "b", "label": "20" }, { "id": "c", "label": "48" }, { "id": "d", "label": "24" } ] }, { "id": "diagrammatic-reasoning-s08-q02", "prompt": "Start with 2. Keep doubling until the number exceeds 30. How many doublings are performed?", "choices": [ { "id": "a", "label": "5" }, { "id": "b", "label": "4" }, { "id": "c", "label": "3" }, { "id": "d", "label": "6" } ] }, { "id": "diagrammatic-reasoning-s08-q03", "prompt": "Start with 100. Repeatedly subtract 15 until the result is 40 or less. What is the final number?", "choices": [ { "id": "a", "label": "40" }, { "id": "b", "label": "25" }, { "id": "c", "label": "55" }, { "id": "d", "label": "45" } ] }, { "id": "diagrammatic-reasoning-s08-q04", "prompt": "Start with 1. Add 3 on each pass and stop as soon as the total reaches 13 or more. How many passes run?", "choices": [ { "id": "a", "label": "3" }, { "id": "b", "label": "5" }, { "id": "c", "label": "4" }, { "id": "d", "label": "6" } ] }, { "id": "diagrammatic-reasoning-s08-q05", "prompt": "Start with the word DIAGRAMS. Remove the last letter repeatedly until exactly 4 letters remain. What is left?", "choices": [ { "id": "a", "label": "DIAG" }, { "id": "b", "label": "DIAGR" }, { "id": "c", "label": "RAMS" }, { "id": "d", "label": "DIA" } ] }, { "id": "diagrammatic-reasoning-s08-q06", "prompt": "A loop applies this rule: if the number is even, halve it; if odd, add 5. Start with 9 and apply the rule exactly 3 times. What results?", "choices": [ { "id": "a", "label": "7" }, { "id": "b", "label": "14" }, { "id": "c", "label": "6" }, { "id": "d", "label": "12" } ] }, { "id": "diagrammatic-reasoning-s08-q07", "prompt": "Start with 5. On odd-numbered passes (1st, 3rd, ...) add 2; on even-numbered passes subtract 1. Run exactly 4 passes. What results?", "choices": [ { "id": "a", "label": "9" }, { "id": "b", "label": "6" }, { "id": "c", "label": "7" }, { "id": "d", "label": "8" } ] }, { "id": "diagrammatic-reasoning-s08-q08", "prompt": "A loop halves the number while it is even. Start with 48. What is the final number?", "choices": [ { "id": "a", "label": "6" }, { "id": "b", "label": "3" }, { "id": "c", "label": "1" }, { "id": "d", "label": "24" } ] }, { "id": "diagrammatic-reasoning-s08-q09", "prompt": "Start with 7. Loop: if the number is odd, add 3; if even, halve it. Stop when the number is below 5. What is the final number?", "choices": [ { "id": "a", "label": "4" }, { "id": "b", "label": "5" }, { "id": "c", "label": "2" }, { "id": "d", "label": "8" } ] }, { "id": "diagrammatic-reasoning-s08-q10", "prompt": "A loop applies this rule: if the number is odd, add 2; stop when the number becomes even. Start with 9. What happens?", "choices": [ { "id": "a", "label": "It stops at 10" }, { "id": "b", "label": "It stops at 11" }, { "id": "c", "label": "It stops after exactly five passes" }, { "id": "d", "label": "It never stops" } ] } ] }, { "id": "diagrammatic-reasoning-s09", "title": "Fault-finding in operator networks", "instructions": "A box may fail by passing its input through unchanged. Compare expected and actual outputs to isolate the fault.", "items": [ { "id": "diagrammatic-reasoning-s09-q01", "prompt": "The pipeline [Add 5] → [Double] receives 3. The expected output is 16, but the actual output is 8. Which box failed by passing its input unchanged?", "choices": [ { "id": "a", "label": "The Add 5 box" }, { "id": "b", "label": "The Double box" }, { "id": "c", "label": "Both boxes" }, { "id": "d", "label": "Neither box" } ] }, { "id": "diagrammatic-reasoning-s09-q02", "prompt": "The pipeline [Reverse] → [Remove the last item] receives A-B-C-D. The expected output is D-C-B, but the actual output is A-B-C. Which box failed by passing its input unchanged?", "choices": [ { "id": "a", "label": "The Reverse box" }, { "id": "b", "label": "The Remove box" }, { "id": "c", "label": "Both boxes" }, { "id": "d", "label": "Neither box" } ] }, { "id": "diagrammatic-reasoning-s09-q03", "prompt": "The pipeline [Subtract 2] → [Triple] receives 6. The expected output is 12, but the actual output is 18. Which box failed by passing its input unchanged?", "choices": [ { "id": "a", "label": "The Triple box" }, { "id": "b", "label": "Both boxes" }, { "id": "c", "label": "The Subtract 2 box" }, { "id": "d", "label": "Neither box" } ] }, { "id": "diagrammatic-reasoning-s09-q04", "prompt": "The pipeline [Toggle shading] → [Rotate 180°] receives a white arrow pointing up. The expected output is a black arrow pointing down, but the actual output is a white arrow pointing down. Which box failed by passing its input unchanged?", "choices": [ { "id": "a", "label": "The Rotate box" }, { "id": "b", "label": "Both boxes" }, { "id": "c", "label": "Neither box" }, { "id": "d", "label": "The Toggle shading box" } ] }, { "id": "diagrammatic-reasoning-s09-q05", "prompt": "The pipeline [Add 1] → [Double] → [Subtract 3] receives 4. The expected output is 7, but the actual output is 5. Exactly one box passed its input unchanged. Which one?", "choices": [ { "id": "a", "label": "The Add 1 box" }, { "id": "b", "label": "The Double box" }, { "id": "c", "label": "The Subtract 3 box" }, { "id": "d", "label": "It cannot be determined" } ] }, { "id": "diagrammatic-reasoning-s09-q06", "prompt": "The pipeline [Double] → [Subtract 4] → [Double] receives 5. The expected output is 12, but the actual output is 20. Exactly one box passed its input unchanged. Which one?", "choices": [ { "id": "a", "label": "The first Double box" }, { "id": "b", "label": "The second Double box" }, { "id": "c", "label": "The Subtract 4 box" }, { "id": "d", "label": "None of the boxes" } ] }, { "id": "diagrammatic-reasoning-s09-q07", "prompt": "A box labelled 'Add 10' receives 7 and outputs 27. Which fault mode best describes its behaviour?", "choices": [ { "id": "a", "label": "It did nothing" }, { "id": "b", "label": "It applied its rule twice" }, { "id": "c", "label": "It subtracted instead of adding" }, { "id": "d", "label": "It worked correctly" } ] }, { "id": "diagrammatic-reasoning-s09-q08", "prompt": "A network splits the input 12 down two paths, top: [Halve]; bottom: [Subtract 8], then adds the two results. The expected output is 10, but the actual output is 16. Which component failed by passing its input unchanged?", "choices": [ { "id": "a", "label": "The Subtract 8 box" }, { "id": "b", "label": "Both boxes" }, { "id": "c", "label": "Neither box" }, { "id": "d", "label": "The Halve box" } ] }, { "id": "diagrammatic-reasoning-s09-q09", "prompt": "The pipeline [Remove the first item] → [Reverse] → [Remove the first item] receives 1-2-3-4. The expected output is 3-2, but the actual output is 3-2-1. Exactly one box passed its input unchanged. Which one?", "choices": [ { "id": "a", "label": "The Reverse box" }, { "id": "b", "label": "The second Remove box" }, { "id": "c", "label": "None of the boxes" }, { "id": "d", "label": "The first Remove box" } ] }, { "id": "diagrammatic-reasoning-s09-q10", "prompt": "A 'Double' box is tested twice. Test 1: input 3 gives output 6. Test 2: input 8 gives output 8. What is the soundest conclusion?", "choices": [ { "id": "a", "label": "It doubled correctly in the first test but passed the input unchanged in the second" }, { "id": "b", "label": "It always works correctly" }, { "id": "c", "label": "It never works correctly" }, { "id": "d", "label": "It halves even numbers" } ] } ] }, { "id": "diagrammatic-reasoning-s10", "title": "Integrated system challenges", "instructions": "These combine rule deduction, ordering, loops, and faults. Verify each stage before moving to the next.", "items": [ { "id": "diagrammatic-reasoning-s10-q01", "prompt": "A white arrow pointing north passes through [Rotate 90° clockwise] → [Toggle shading] → [Rotate 90° clockwise]. What comes out?", "choices": [ { "id": "a", "label": "A white arrow pointing south" }, { "id": "b", "label": "A black arrow pointing north" }, { "id": "c", "label": "A black arrow pointing south" }, { "id": "d", "label": "A black arrow pointing west" } ] }, { "id": "diagrammatic-reasoning-s10-q02", "prompt": "Operator ◆ doubles its input; operator ● adds a fixed number. The pipeline [◆] → [●] turns 6 into 15 and 10 into 23. What does the reversed pipeline [●] → [◆] give for the input 8?", "choices": [ { "id": "a", "label": "19" }, { "id": "b", "label": "16" }, { "id": "c", "label": "13" }, { "id": "d", "label": "22" } ] }, { "id": "diagrammatic-reasoning-s10-q03", "prompt": "In a network, the numbers 3 and 5 enter a [Multiply] box. Its result and the number 4 then enter a [Difference] box that subtracts the smaller from the larger. What is the final output?", "choices": [ { "id": "a", "label": "19" }, { "id": "b", "label": "11" }, { "id": "c", "label": "60" }, { "id": "d", "label": "7" } ] }, { "id": "diagrammatic-reasoning-s10-q04", "prompt": "A network routes by parity: even inputs go through [Square]; odd inputs go through [Add 7, then Halve]. The input 9 enters, and the result then passes through the network once more. What is the final output?", "choices": [ { "id": "a", "label": "64" }, { "id": "b", "label": "8" }, { "id": "c", "label": "16" }, { "id": "d", "label": "32" } ] }, { "id": "diagrammatic-reasoning-s10-q05", "prompt": "Analogy: a white arrow pointing up is to a white arrow pointing right as a black arrow pointing left is to what?", "choices": [ { "id": "a", "label": "A black arrow pointing down" }, { "id": "b", "label": "A white arrow pointing up" }, { "id": "c", "label": "A black arrow pointing right" }, { "id": "d", "label": "A black arrow pointing up" } ] }, { "id": "diagrammatic-reasoning-s10-q06", "prompt": "The pipeline [Add 2] → [Double] → [Subtract 1] should turn 5 into 13, but a test run produced 9. Exactly one box passes its input unchanged. What output will the same faulty machine give for the input 10?", "choices": [ { "id": "a", "label": "23" }, { "id": "b", "label": "21" }, { "id": "c", "label": "19" }, { "id": "d", "label": "20" } ] }, { "id": "diagrammatic-reasoning-s10-q07", "prompt": "Start with 2. Each pass sends the value through [Double] then [Add 1]. Repeat passes until the value exceeds 20, then stop. What is the final value?", "choices": [ { "id": "a", "label": "23" }, { "id": "b", "label": "11" }, { "id": "c", "label": "22" }, { "id": "d", "label": "21" } ] }, { "id": "diagrammatic-reasoning-s10-q08", "prompt": "A machine has a single store. When a number arrives: if the store is empty, the number is stored; otherwise the machine outputs the sum of the store and the arrival, then clears the store. The inputs are 3, 4, 6, 2 in that order. What is the second number the machine outputs?", "choices": [ { "id": "a", "label": "7" }, { "id": "b", "label": "8" }, { "id": "c", "label": "6" }, { "id": "d", "label": "9" } ] }, { "id": "diagrammatic-reasoning-s10-q09", "prompt": "A figure series shows: (1 black dot, 8 white dots), (2 black, 6 white), (3 black, 4 white), (4 black, 2 white). How many dots in total does the fifth figure contain?", "choices": [ { "id": "a", "label": "7" }, { "id": "b", "label": "6" }, { "id": "c", "label": "5" }, { "id": "d", "label": "9" } ] }, { "id": "diagrammatic-reasoning-s10-q10", "prompt": "Operator ★ turns 3 into 9 and 5 into 15. Operator ✦ turns 12 into 6 and 8 into 4. Starting with 4, apply ★, then ✦, then ★, then ✦. What is the final value?", "choices": [ { "id": "a", "label": "12" }, { "id": "b", "label": "9" }, { "id": "c", "label": "18" }, { "id": "d", "label": "6" } ] } ] } ] }, "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": [ "diagrammatic-reasoning-s01-q01", "diagrammatic-reasoning-s01-q02", "diagrammatic-reasoning-s01-q03", "diagrammatic-reasoning-s01-q04", "diagrammatic-reasoning-s01-q05", "diagrammatic-reasoning-s01-q06", "diagrammatic-reasoning-s01-q07", "diagrammatic-reasoning-s01-q08", "diagrammatic-reasoning-s01-q09", "diagrammatic-reasoning-s01-q10", "diagrammatic-reasoning-s02-q01", "diagrammatic-reasoning-s02-q02", "diagrammatic-reasoning-s02-q03", "diagrammatic-reasoning-s02-q04", "diagrammatic-reasoning-s02-q05", "diagrammatic-reasoning-s02-q06", "diagrammatic-reasoning-s02-q07", "diagrammatic-reasoning-s02-q08", "diagrammatic-reasoning-s02-q09", "diagrammatic-reasoning-s02-q10", "diagrammatic-reasoning-s03-q01", "diagrammatic-reasoning-s03-q02", "diagrammatic-reasoning-s03-q03", "diagrammatic-reasoning-s03-q04", "diagrammatic-reasoning-s03-q05", 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"diagrammatic-reasoning-s09-q04", "diagrammatic-reasoning-s09-q05", "diagrammatic-reasoning-s09-q06", "diagrammatic-reasoning-s09-q07", "diagrammatic-reasoning-s09-q08", "diagrammatic-reasoning-s09-q09", "diagrammatic-reasoning-s09-q10", "diagrammatic-reasoning-s10-q01", "diagrammatic-reasoning-s10-q02", "diagrammatic-reasoning-s10-q03", "diagrammatic-reasoning-s10-q04", "diagrammatic-reasoning-s10-q05", "diagrammatic-reasoning-s10-q06", "diagrammatic-reasoning-s10-q07", "diagrammatic-reasoning-s10-q08", "diagrammatic-reasoning-s10-q09", "diagrammatic-reasoning-s10-q10" ] }, "answerKey": { "title": "Answer key", "items": [ { "itemId": "diagrammatic-reasoning-s01-q01", "correctChoiceId": "c", "correctChoiceLabel": "13" }, { "itemId": "diagrammatic-reasoning-s01-q02", "correctChoiceId": "b", "correctChoiceLabel": "14" }, { "itemId": "diagrammatic-reasoning-s01-q03", "correctChoiceId": "c", "correctChoiceLabel": "R-Q-P" }, { "itemId": "diagrammatic-reasoning-s01-q04", "correctChoiceId": "a", "correctChoiceLabel": "apple, pear" }, { "itemId": "diagrammatic-reasoning-s01-q05", "correctChoiceId": "d", "correctChoiceLabel": "Right" }, { "itemId": "diagrammatic-reasoning-s01-q06", "correctChoiceId": "a", "correctChoiceLabel": "■ ● ▲ ★" }, { "itemId": "diagrammatic-reasoning-s01-q07", "correctChoiceId": "b", "correctChoiceLabel": "13" }, { "itemId": "diagrammatic-reasoning-s01-q08", "correctChoiceId": "d", "correctChoiceLabel": "A black triangle" }, { "itemId": "diagrammatic-reasoning-s01-q09", "correctChoiceId": "b", "correctChoiceLabel": "A-B-A-B" }, { "itemId": "diagrammatic-reasoning-s01-q10", "correctChoiceId": "a", "correctChoiceLabel": "0" }, { "itemId": "diagrammatic-reasoning-s02-q01", "correctChoiceId": "b", "correctChoiceLabel": "16" }, { "itemId": "diagrammatic-reasoning-s02-q02", "correctChoiceId": "a", "correctChoiceLabel": "4" }, { "itemId": "diagrammatic-reasoning-s02-q03", "correctChoiceId": "d", "correctChoiceLabel": "T-A" }, { "itemId": "diagrammatic-reasoning-s02-q04", "correctChoiceId": "c", "correctChoiceLabel": "West" }, { "itemId": "diagrammatic-reasoning-s02-q05", "correctChoiceId": "b", "correctChoiceLabel": "8, 6, 4" }, { "itemId": "diagrammatic-reasoning-s02-q06", "correctChoiceId": "d", "correctChoiceLabel": "10" }, { "itemId": "diagrammatic-reasoning-s02-q07", "correctChoiceId": "a", "correctChoiceLabel": "A black circle" }, { "itemId": "diagrammatic-reasoning-s02-q08", "correctChoiceId": "c", "correctChoiceLabel": "SATR" }, { "itemId": "diagrammatic-reasoning-s02-q09", "correctChoiceId": "c", "correctChoiceLabel": "7" }, { "itemId": "diagrammatic-reasoning-s02-q10", "correctChoiceId": "b", "correctChoiceLabel": "14" }, { "itemId": "diagrammatic-reasoning-s03-q01", "correctChoiceId": "b", "correctChoiceLabel": "It doubles" }, { "itemId": "diagrammatic-reasoning-s03-q02", "correctChoiceId": "d", "correctChoiceLabel": "It subtracts 3" }, { "itemId": "diagrammatic-reasoning-s03-q03", "correctChoiceId": "a", "correctChoiceLabel": "It reverses all the letters" }, { "itemId": "diagrammatic-reasoning-s03-q04", "correctChoiceId": "c", "correctChoiceLabel": "It squares" }, { "itemId": "diagrammatic-reasoning-s03-q05", "correctChoiceId": "b", "correctChoiceLabel": "It copies the first symbol onto the end" }, { "itemId": "diagrammatic-reasoning-s03-q06", "correctChoiceId": "a", "correctChoiceLabel": "It doubles, then adds 1" }, { "itemId": "diagrammatic-reasoning-s03-q07", "correctChoiceId": "d", "correctChoiceLabel": "It swaps the shading but keeps the shape" }, { "itemId": "diagrammatic-reasoning-s03-q08", "correctChoiceId": "c", "correctChoiceLabel": "It halves" }, { "itemId": "diagrammatic-reasoning-s03-q09", "correctChoiceId": "a", "correctChoiceLabel": "It removes the last letter" }, { "itemId": "diagrammatic-reasoning-s03-q10", "correctChoiceId": "b", "correctChoiceLabel": "It cubes" }, { "itemId": "diagrammatic-reasoning-s04-q01", "correctChoiceId": "d", "correctChoiceLabel": "5 dots" }, { "itemId": "diagrammatic-reasoning-s04-q02", "correctChoiceId": "a", "correctChoiceLabel": "Black" }, { "itemId": "diagrammatic-reasoning-s04-q03", "correctChoiceId": "c", "correctChoiceLabel": "Left" }, { "itemId": "diagrammatic-reasoning-s04-q04", "correctChoiceId": "b", "correctChoiceLabel": "5 black dots" }, { "itemId": "diagrammatic-reasoning-s04-q05", "correctChoiceId": "d", "correctChoiceLabel": "Hexagon" }, { "itemId": "diagrammatic-reasoning-s04-q06", "correctChoiceId": "b", "correctChoiceLabel": "Bottom-left corner" }, { "itemId": "diagrammatic-reasoning-s04-q07", "correctChoiceId": "a", "correctChoiceLabel": "18" }, { "itemId": "diagrammatic-reasoning-s04-q08", "correctChoiceId": "c", "correctChoiceLabel": "O" }, { "itemId": "diagrammatic-reasoning-s04-q09", "correctChoiceId": "d", "correctChoiceLabel": "A small arrow pointing left" }, { "itemId": "diagrammatic-reasoning-s04-q10", "correctChoiceId": "c", "correctChoiceLabel": "5" }, { "itemId": "diagrammatic-reasoning-s05-q01", "correctChoiceId": "c", "correctChoiceLabel": "10" }, { "itemId": "diagrammatic-reasoning-s05-q02", "correctChoiceId": "a", "correctChoiceLabel": "6" }, { "itemId": "diagrammatic-reasoning-s05-q03", "correctChoiceId": "b", "correctChoiceLabel": "5" }, { "itemId": "diagrammatic-reasoning-s05-q04", "correctChoiceId": "d", "correctChoiceLabel": "GNARO" }, { "itemId": "diagrammatic-reasoning-s05-q05", "correctChoiceId": "a", "correctChoiceLabel": "6" }, { "itemId": "diagrammatic-reasoning-s05-q06", "correctChoiceId": "c", "correctChoiceLabel": "Depot C" }, { "itemId": "diagrammatic-reasoning-s05-q07", "correctChoiceId": "d", "correctChoiceLabel": "A 1.8 kg parcel, not fragile" }, { "itemId": "diagrammatic-reasoning-s05-q08", "correctChoiceId": "b", "correctChoiceLabel": "14" }, { "itemId": "diagrammatic-reasoning-s05-q09", "correctChoiceId": "b", "correctChoiceLabel": "13" }, { "itemId": "diagrammatic-reasoning-s05-q10", "correctChoiceId": "d", "correctChoiceLabel": "15" }, { "itemId": "diagrammatic-reasoning-s06-q01", "correctChoiceId": "a", "correctChoiceLabel": "Green" }, { "itemId": "diagrammatic-reasoning-s06-q02", "correctChoiceId": "c", "correctChoiceLabel": "Open" }, { "itemId": "diagrammatic-reasoning-s06-q03", "correctChoiceId": "d", "correctChoiceLabel": "Printing" }, { "itemId": "diagrammatic-reasoning-s06-q04", "correctChoiceId": "b", "correctChoiceLabel": "Printing" }, { "itemId": "diagrammatic-reasoning-s06-q05", "correctChoiceId": "c", "correctChoiceLabel": "Floor 4" }, { "itemId": "diagrammatic-reasoning-s06-q06", "correctChoiceId": "a", "correctChoiceLabel": "Spin" }, { "itemId": "diagrammatic-reasoning-s06-q07", "correctChoiceId": "b", "correctChoiceLabel": "Locked" }, { "itemId": "diagrammatic-reasoning-s06-q08", "correctChoiceId": "d", "correctChoiceLabel": "Stations 1 and 3" }, { "itemId": "diagrammatic-reasoning-s06-q09", "correctChoiceId": "a", "correctChoiceLabel": "Fresh" }, { "itemId": "diagrammatic-reasoning-s06-q10", "correctChoiceId": "c", "correctChoiceLabel": "20p" }, { "itemId": "diagrammatic-reasoning-s07-q01", "correctChoiceId": "b", "correctChoiceLabel": "12" }, { "itemId": "diagrammatic-reasoning-s07-q02", "correctChoiceId": "d", "correctChoiceLabel": "T-S-R" }, { "itemId": "diagrammatic-reasoning-s07-q03", "correctChoiceId": "a", "correctChoiceLabel": "11" }, { "itemId": "diagrammatic-reasoning-s07-q04", "correctChoiceId": "c", "correctChoiceLabel": "Y-Z" }, { "itemId": "diagrammatic-reasoning-s07-q05", "correctChoiceId": "c", "correctChoiceLabel": "It multiplies by 3" }, { "itemId": "diagrammatic-reasoning-s07-q06", "correctChoiceId": "d", "correctChoiceLabel": "Add 5" }, { "itemId": "diagrammatic-reasoning-s07-q07", "correctChoiceId": "b", "correctChoiceLabel": "A black arrow pointing right" }, { "itemId": "diagrammatic-reasoning-s07-q08", "correctChoiceId": "a", "correctChoiceLabel": "Halve first, then Add 2" }, { "itemId": "diagrammatic-reasoning-s07-q09", "correctChoiceId": "d", "correctChoiceLabel": "It removes the last item" }, { "itemId": "diagrammatic-reasoning-s07-q10", "correctChoiceId": "a", "correctChoiceLabel": "9" }, { "itemId": "diagrammatic-reasoning-s08-q01", "correctChoiceId": "d", "correctChoiceLabel": "24" }, { "itemId": "diagrammatic-reasoning-s08-q02", "correctChoiceId": "b", "correctChoiceLabel": "4" }, { "itemId": "diagrammatic-reasoning-s08-q03", "correctChoiceId": "a", "correctChoiceLabel": "40" }, { "itemId": "diagrammatic-reasoning-s08-q04", "correctChoiceId": "c", "correctChoiceLabel": "4" }, { "itemId": "diagrammatic-reasoning-s08-q05", "correctChoiceId": "a", "correctChoiceLabel": "DIAG" }, { "itemId": "diagrammatic-reasoning-s08-q06", "correctChoiceId": "d", "correctChoiceLabel": "12" }, { "itemId": "diagrammatic-reasoning-s08-q07", "correctChoiceId": "c", "correctChoiceLabel": "7" }, { "itemId": "diagrammatic-reasoning-s08-q08", "correctChoiceId": "b", "correctChoiceLabel": "3" }, { "itemId": "diagrammatic-reasoning-s08-q09", "correctChoiceId": "a", "correctChoiceLabel": "4" }, { "itemId": "diagrammatic-reasoning-s08-q10", "correctChoiceId": "d", "correctChoiceLabel": "It never stops" }, { "itemId": "diagrammatic-reasoning-s09-q01", "correctChoiceId": "b", "correctChoiceLabel": "The Double box" }, { "itemId": "diagrammatic-reasoning-s09-q02", "correctChoiceId": "a", "correctChoiceLabel": "The Reverse box" }, { "itemId": "diagrammatic-reasoning-s09-q03", "correctChoiceId": "c", "correctChoiceLabel": "The Subtract 2 box" }, { "itemId": "diagrammatic-reasoning-s09-q04", "correctChoiceId": "d", "correctChoiceLabel": "The Toggle shading box" }, { "itemId": "diagrammatic-reasoning-s09-q05", "correctChoiceId": "a", "correctChoiceLabel": "The Add 1 box" }, { "itemId": "diagrammatic-reasoning-s09-q06", "correctChoiceId": "c", "correctChoiceLabel": "The Subtract 4 box" }, { "itemId": "diagrammatic-reasoning-s09-q07", "correctChoiceId": "b", "correctChoiceLabel": "It applied its rule twice" }, { "itemId": "diagrammatic-reasoning-s09-q08", "correctChoiceId": "d", "correctChoiceLabel": "The Halve box" }, { "itemId": "diagrammatic-reasoning-s09-q09", "correctChoiceId": "d", "correctChoiceLabel": "The first Remove box" }, { "itemId": "diagrammatic-reasoning-s09-q10", "correctChoiceId": "a", "correctChoiceLabel": "It doubled correctly in the first test but passed the input unchanged in the second" }, { "itemId": "diagrammatic-reasoning-s10-q01", "correctChoiceId": "c", "correctChoiceLabel": "A black arrow pointing south" }, { "itemId": "diagrammatic-reasoning-s10-q02", "correctChoiceId": "d", "correctChoiceLabel": "22" }, { "itemId": "diagrammatic-reasoning-s10-q03", "correctChoiceId": "b", "correctChoiceLabel": "11" }, { "itemId": "diagrammatic-reasoning-s10-q04", "correctChoiceId": "a", "correctChoiceLabel": "64" }, { "itemId": "diagrammatic-reasoning-s10-q05", "correctChoiceId": "d", "correctChoiceLabel": "A black arrow pointing up" }, { "itemId": "diagrammatic-reasoning-s10-q06", "correctChoiceId": "c", "correctChoiceLabel": "19" }, { "itemId": "diagrammatic-reasoning-s10-q07", "correctChoiceId": "a", "correctChoiceLabel": "23" }, { "itemId": "diagrammatic-reasoning-s10-q08", "correctChoiceId": "b", "correctChoiceLabel": "8" }, { "itemId": "diagrammatic-reasoning-s10-q09", "correctChoiceId": "c", "correctChoiceLabel": "5" }, { "itemId": "diagrammatic-reasoning-s10-q10", "correctChoiceId": "b", "correctChoiceLabel": "9" } ] }, "workedExplanations": { "title": "Worked explanations", "items": [ { "itemId": "diagrammatic-reasoning-s01-q01", "explanation": "An 'Add 4' box outputs its input plus 4, so 9 becomes 9 + 4 = 13." }, { "itemId": "diagrammatic-reasoning-s01-q02", "explanation": "Doubling multiplies the input by 2, so 7 becomes 14." }, { "itemId": "diagrammatic-reasoning-s01-q03", "explanation": "Reversing writes the sequence back to front, so P-Q-R becomes R-Q-P. The middle item stays in place for a three-item sequence." }, { "itemId": "diagrammatic-reasoning-s01-q04", "explanation": "The box deletes only the final item (plum), leaving the rest in their original order." }, { "itemId": "diagrammatic-reasoning-s01-q05", "explanation": "A quarter turn clockwise moves an upward arrow to point right, imagine turning a clock hand from 12 to 3." }, { "itemId": "diagrammatic-reasoning-s01-q06", "explanation": "Only the two end symbols trade places (★ and ■); the middle symbols stay exactly where they were." }, { "itemId": "diagrammatic-reasoning-s01-q07", "explanation": "Halving divides the input by 2, so 26 becomes 13." }, { "itemId": "diagrammatic-reasoning-s01-q08", "explanation": "The box changes shading only, so the triangle keeps its shape but flips from white to black." }, { "itemId": "diagrammatic-reasoning-s01-q09", "explanation": "Repeating the whole sequence writes the complete run again after itself, giving A-B followed by A-B, not each symbol doubled in place." }, { "itemId": "diagrammatic-reasoning-s01-q10", "explanation": "6 − 6 = 0, a valid output; an operator can produce zero." }, { "itemId": "diagrammatic-reasoning-s02-q01", "explanation": "Work left to right: 5 + 3 = 8, then 8 × 2 = 16." }, { "itemId": "diagrammatic-reasoning-s02-q02", "explanation": "12 ÷ 2 = 6, then 6 − 2 = 4." }, { "itemId": "diagrammatic-reasoning-s02-q03", "explanation": "Reversing gives T-A-C; removing the last letter of that result leaves T-A. Apply each box to the previous box's output, not to the original input." }, { "itemId": "diagrammatic-reasoning-s02-q04", "explanation": "North turned 90° clockwise points east; a further 180° turn points it the opposite way, west." }, { "itemId": "diagrammatic-reasoning-s02-q05", "explanation": "Removing the first item leaves 4, 6, 8; reversing that gives 8, 6, 4." }, { "itemId": "diagrammatic-reasoning-s02-q06", "explanation": "3 squared is 9, and 9 + 1 = 10." }, { "itemId": "diagrammatic-reasoning-s02-q07", "explanation": "Toggling makes the circle black, and rotating a circle produces no visible change. Some operators have no effect on symmetric figures." }, { "itemId": "diagrammatic-reasoning-s02-q08", "explanation": "Swapping the end letters of STAR gives RTAS; reversing RTAS gives SATR. Track the intermediate result carefully at each stage." }, { "itemId": "diagrammatic-reasoning-s02-q09", "explanation": "18 − 4 = 14, then 14 ÷ 2 = 7." }, { "itemId": "diagrammatic-reasoning-s02-q10", "explanation": "Order matters in a pipeline: doubling first gives 12, then adding 2 gives 14, a different result from the original wiring." }, { "itemId": "diagrammatic-reasoning-s03-q01", "explanation": "Test each candidate against every pair: adding 3 fits 3→6 but fails 5→10, and squaring would turn 9 into 81. Only doubling fits all three examples." }, { "itemId": "diagrammatic-reasoning-s03-q02", "explanation": "Halving fits 6→3 but fails 10→7; subtracting 3 is the only rule that fits every pair." }, { "itemId": "diagrammatic-reasoning-s03-q03", "explanation": "For a three-letter word several rules look identical, so use the longer example to separate them: swapping only the end letters of STOP would give PTOS, not POTS. Full reversal fits both." }, { "itemId": "diagrammatic-reasoning-s03-q04", "explanation": "Multiplying by 4 fits 4→16 but fails 5→25, and adding 12 fails 5→25 too. Each output is the input multiplied by itself, so the box squares." }, { "itemId": "diagrammatic-reasoning-s03-q05", "explanation": "In both examples the output is the original sequence with its opening symbol appended at the end, nothing else moves." }, { "itemId": "diagrammatic-reasoning-s03-q06", "explanation": "Adding 8 fits 7→15 but fails 10→21, and tripling-minus-6 also fails 10→21. Doubling then adding 1 fits all three pairs. Always check every example, not just the first." }, { "itemId": "diagrammatic-reasoning-s03-q07", "explanation": "Both examples keep their shape while black and white exchange, so the rule acts on shading alone." }, { "itemId": "diagrammatic-reasoning-s03-q08", "explanation": "Subtracting 6 fits 12→6 but fails 20→10; each output is exactly half its input, so the box halves." }, { "itemId": "diagrammatic-reasoning-s03-q09", "explanation": "Every output is the input with just its final letter missing: removing vowels would have turned RAIN into RN." }, { "itemId": "diagrammatic-reasoning-s03-q10", "explanation": "All four candidate rules turn 2 into 8, but only cubing also turns 3 into 27: a single example rarely pins down a rule, so seek a second one before deciding." }, { "itemId": "diagrammatic-reasoning-s04-q01", "explanation": "The count rises by one dot per frame, so the next frame shows 5 dots." }, { "itemId": "diagrammatic-reasoning-s04-q02", "explanation": "The shading alternates every frame, and the last square shown was white, so black follows." }, { "itemId": "diagrammatic-reasoning-s04-q03", "explanation": "Each frame turns the arrow 90° clockwise (up → right → down), so the next quarter turn points it left." }, { "itemId": "diagrammatic-reasoning-s04-q04", "explanation": "Two features change independently: the count rises by one each frame while the shading alternates. After 4 white comes 5 black." }, { "itemId": "diagrammatic-reasoning-s04-q05", "explanation": "Each shape has one more side than the last (3, 4, 5), so a six-sided hexagon comes next." }, { "itemId": "diagrammatic-reasoning-s04-q06", "explanation": "The star moves one corner clockwise each frame, so from bottom-right it reaches bottom-left." }, { "itemId": "diagrammatic-reasoning-s04-q07", "explanation": "Two rules alternate: double, then subtract 1 (2→4→3→6→5→10→9). The next step doubles again: 9 × 2 = 18." }, { "itemId": "diagrammatic-reasoning-s04-q08", "explanation": "The gaps grow by one each step: +2, +3, +4, so the next gap is +5. Five letters past J is O." }, { "itemId": "diagrammatic-reasoning-s04-q09", "explanation": "Track each feature separately: the size cycle returns to small, while the rotation continues from down to left." }, { "itemId": "diagrammatic-reasoning-s04-q10", "explanation": "Each row rises by 1 from left to right (and each row starts one higher than the row above), so the final cell holds 5." }, { "itemId": "diagrammatic-reasoning-s05-q01", "explanation": "7 is odd, so the No branch applies: 7 + 3 = 10." }, { "itemId": "diagrammatic-reasoning-s05-q02", "explanation": "12 is greater than 10, so it is halved to 6." }, { "itemId": "diagrammatic-reasoning-s05-q03", "explanation": "9 is odd, so it becomes 10; 10 is greater than 8, so subtracting 5 gives 5. Re-test the condition on the updated value, not the original." }, { "itemId": "diagrammatic-reasoning-s05-q04", "explanation": "ORANGE has 6 letters, so it becomes ORANG; ORANG starts with the vowel O, so it is reversed to GNARO." }, { "itemId": "diagrammatic-reasoning-s05-q05", "explanation": "15 is a multiple of 3, giving 5; 5 is odd, so adding 1 gives 6." }, { "itemId": "diagrammatic-reasoning-s05-q06", "explanation": "At 1.5 kg the parcel passes the weight test, so the fragile question decides: fragile parcels go to Depot C." }, { "itemId": "diagrammatic-reasoning-s05-q07", "explanation": "Weight is tested first, so the 2.5 kg fragile parcel still goes to Depot B. Only a parcel at 2 kg or under that is not fragile reaches Depot A." }, { "itemId": "diagrammatic-reasoning-s05-q08", "explanation": "24 halves to 12; 12 divides by 3 to give 4; 4 is not greater than 5, so adding 10 gives 14." }, { "itemId": "diagrammatic-reasoning-s05-q09", "explanation": "Check each backwards path for consistency: an even input would be 9, but 9 is odd, contradiction. An odd input of 13 gives 13 + 5 = 18 and stays consistent." }, { "itemId": "diagrammatic-reasoning-s05-q10", "explanation": "6 is even, so the pair becomes (9, 6); the sum 15 exceeds 14, so the sum itself is output. Note that swapping never changes a sum." }, { "itemId": "diagrammatic-reasoning-s06-q01", "explanation": "From Amber, one change reaches Red and a second completes the cycle to Green." }, { "itemId": "diagrammatic-reasoning-s06-q02", "explanation": "Turning the key moves Locked to Closed, and pushing then opens the door." }, { "itemId": "diagrammatic-reasoning-s06-q03", "explanation": "The coin moves the machine to Ready and the button press moves it on to Printing." }, { "itemId": "diagrammatic-reasoning-s06-q04", "explanation": "The first press does nothing in Idle; the coin then moves it to Ready and the second press starts Printing. Signals with no listed transition are simply ignored." }, { "itemId": "diagrammatic-reasoning-s06-q05", "explanation": "Trace floor by floor: 2 → 3 → 4 → 3 → 4." }, { "itemId": "diagrammatic-reasoning-s06-q06", "explanation": "Fill advances to Wash, then Rinse; the hold keeps it at Rinse; the final advance reaches Spin." }, { "itemId": "diagrammatic-reasoning-s06-q07", "explanation": "The first coin unlocks it, the second coin is ignored, the first push relocks it, and the second push is ignored, ending Locked." }, { "itemId": "diagrammatic-reasoning-s06-q08", "explanation": "Every crate passes through Station 1 first; crate 8 is even, so it is routed on to Station 3 and never sees Station 2." }, { "itemId": "diagrammatic-reasoning-s06-q09", "explanation": "Two tasks drop the status to Tired; the third task only counts one of two; the rest restores Fresh and clears the count; the final task leaves the status still Fresh." }, { "itemId": "diagrammatic-reasoning-s06-q10", "explanation": "The second 20p lifts credit to 40p, triggering a vend that leaves 10p; the final 10p brings credit to 20p, below the vend threshold." }, { "itemId": "diagrammatic-reasoning-s07-q01", "explanation": "Both examples double their input, so ◆ turns 6 into 12." }, { "itemId": "diagrammatic-reasoning-s07-q02", "explanation": "Both examples reverse the sequence, so R-S-T becomes T-S-R." }, { "itemId": "diagrammatic-reasoning-s07-q03", "explanation": "● adds 3 in both examples, so the pipeline gives 4 × 2 = 8, then 8 + 3 = 11." }, { "itemId": "diagrammatic-reasoning-s07-q04", "explanation": "In both examples only the first item disappears, so ▲ removes the opening item and X-Y-Z becomes Y-Z." }, { "itemId": "diagrammatic-reasoning-s07-q05", "explanation": "Squaring fits 3→9 but fails 5→15, and adding 6 fails 5→15 too, only multiplying by 3 fits both examples." }, { "itemId": "diagrammatic-reasoning-s07-q06", "explanation": "P turns 2 into 4 and 5 into 10, so Q must turn 4 into 9 and 10 into 15, adding 5 fits both runs." }, { "itemId": "diagrammatic-reasoning-s07-q07", "explanation": "The rotation turns the arrow to point right, and the toggle then flips it from white to black." }, { "itemId": "diagrammatic-reasoning-s07-q08", "explanation": "Test both wirings: halving first gives 3 then 5, while adding 2 first gives 8 then 4, only halve-then-add matches the observed output." }, { "itemId": "diagrammatic-reasoning-s07-q09", "explanation": "Compute the intermediate stage first: reversing gives 2-7-4 and 5-1, so ◇ must drop the final item to leave 2-7 and 5." }, { "itemId": "diagrammatic-reasoning-s07-q10", "explanation": "Work backwards: the final Double must have received 7, so X turned 10 into 7: it subtracts 3, turning 12 into 9." }, { "itemId": "diagrammatic-reasoning-s08-q01", "explanation": "3 → 6 → 12 → 24; 24 is the first value over 20, and the loop stops there rather than doubling again." }, { "itemId": "diagrammatic-reasoning-s08-q02", "explanation": "2 → 4 → 8 → 16 → 32, four doublings bring the number past 30." }, { "itemId": "diagrammatic-reasoning-s08-q03", "explanation": "100 → 85 → 70 → 55 → 40; the condition '40 or less' is met exactly at 40, so no further pass runs." }, { "itemId": "diagrammatic-reasoning-s08-q04", "explanation": "1 → 4 → 7 → 10 → 13: four additions reach the threshold exactly." }, { "itemId": "diagrammatic-reasoning-s08-q05", "explanation": "DIAGRAMS has 8 letters, so four removals from the end leave the first four: DIAG." }, { "itemId": "diagrammatic-reasoning-s08-q06", "explanation": "9 is odd → 14; 14 is even → 7; 7 is odd → 12. Re-test the even/odd condition on each new value." }, { "itemId": "diagrammatic-reasoning-s08-q07", "explanation": "Track the pass number separately from the value: 5 → 7 → 6 → 8 → 7 after passes 1 to 4." }, { "itemId": "diagrammatic-reasoning-s08-q08", "explanation": "48 → 24 → 12 → 6 → 3; the loop stops at 3 because the condition 'while even' finally fails." }, { "itemId": "diagrammatic-reasoning-s08-q09", "explanation": "7 → 10 → 5 → 8 → 4. Note that 5 is not below 5, so the loop must continue past it. Read stopping conditions literally." }, { "itemId": "diagrammatic-reasoning-s08-q10", "explanation": "Adding 2 to an odd number always gives another odd number, so the stopping condition can never be met, checking whether a loop can terminate is part of reading a process diagram." }, { "itemId": "diagrammatic-reasoning-s09-q01", "explanation": "Simulate each fault: with Add 5 broken the output would be 6, and with both broken it would be 3. Only a broken Double explains 8, since 3 + 5 = 8 passed straight through." }, { "itemId": "diagrammatic-reasoning-s09-q02", "explanation": "If Reverse did nothing, the Remove box would trim A-B-C-D to A-B-C. Exactly what was observed. A broken Remove box would instead have produced D-C-B-A." }, { "itemId": "diagrammatic-reasoning-s09-q03", "explanation": "With Subtract 2 broken, the Triple box receives 6 unchanged and outputs 18, matching the observation. A broken Triple box would have given 4." }, { "itemId": "diagrammatic-reasoning-s09-q04", "explanation": "The rotation clearly happened (the arrow points down), but the shading never flipped, so the toggle box passed its input through untouched." }, { "itemId": "diagrammatic-reasoning-s09-q05", "explanation": "Simulate each single fault: a broken Add 1 gives 4 → 8 → 5; a broken Double gives 2; a broken Subtract 3 gives 10. Only the first matches the actual output of 5." }, { "itemId": "diagrammatic-reasoning-s09-q06", "explanation": "A broken first Double gives 5 → 1 → 2; a broken second Double gives 6; a broken Subtract 4 gives 10 → 10 → 20, which matches the observation." }, { "itemId": "diagrammatic-reasoning-s09-q07", "explanation": "Correct behaviour would give 17 and doing nothing would give 7; the observed 27 equals 7 + 10 + 10, the rule applied twice over." }, { "itemId": "diagrammatic-reasoning-s09-q08", "explanation": "With Halve broken the sum is 12 + 4 = 16, matching the observation; a broken Subtract 8 would give 6 + 12 = 18 and both broken would give 24." }, { "itemId": "diagrammatic-reasoning-s09-q09", "explanation": "With the first Remove broken, the full list is reversed to 4-3-2-1 and then trimmed to 3-2-1: the observed result. A broken Reverse would give 3-4, and a broken second Remove would give 4-3-2." }, { "itemId": "diagrammatic-reasoning-s09-q10", "explanation": "Judge each run separately against its expected output: 6 matches 3 doubled, but 8 does not match 16, an intermittent fault that only some test runs reveal." }, { "itemId": "diagrammatic-reasoning-s10-q01", "explanation": "Stage by stage: the arrow turns east, is toggled to black, then turns south. The two quarter turns combine into a half turn regardless of the toggle between them." }, { "itemId": "diagrammatic-reasoning-s10-q02", "explanation": "From the examples, ● adds 3 (12 → 15 and 20 → 23). Reversing the order changes the result: 8 + 3 = 11, then doubled to 22." }, { "itemId": "diagrammatic-reasoning-s10-q03", "explanation": "3 × 5 = 15, and the difference between 15 and 4 is 11." }, { "itemId": "diagrammatic-reasoning-s10-q04", "explanation": "First pass: 9 is odd, so (9 + 7) ÷ 2 = 8. Second pass: 8 is even, so it is squared to 64. Re-test the routing condition on the new value." }, { "itemId": "diagrammatic-reasoning-s10-q05", "explanation": "The first pair shows a 90° clockwise rotation with shading preserved; rotating a left-pointing arrow 90° clockwise points it up, still black." }, { "itemId": "diagrammatic-reasoning-s10-q06", "explanation": "Only a broken Add 2 explains the test: 5 → 10 → 9 (a broken Double gives 6 and a broken Subtract 1 gives 14). Through the same fault, 10 doubles to 20 and then loses 1, giving 19." }, { "itemId": "diagrammatic-reasoning-s10-q07", "explanation": "Each full pass maps n to 2n + 1: 2 → 5 → 11 → 23, and 23 is the first value past 20." }, { "itemId": "diagrammatic-reasoning-s10-q08", "explanation": "The machine pairs arrivals: 3 is stored, 4 triggers the output 7; then 6 is stored and 2 triggers the output 8." }, { "itemId": "diagrammatic-reasoning-s10-q09", "explanation": "Black dots rise by 1 while white dots fall by 2 each frame, so the fifth figure has 5 black and 0 white, 5 dots in total." }, { "itemId": "diagrammatic-reasoning-s10-q10", "explanation": "★ triples and ✦ halves, so the chain runs 4 → 12 → 6 → 18 → 9. Deduce each operator from its examples first, then trace the chain one step at a time." } ] } }