Diagrammatic reasoning: transformations, flows, and rule diagrams: open practice pack ##################################################################################### 100 untimed questions across 10 authored sections. Pack: cognitive-skills-diagrammatic-reasoning Source: cognitive-skills Pack version: v1 Worksheet items: 100 Authored hints: 0 Worked explanations: 100 ! 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. ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. Learner worksheet ================= 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. Reading single-step flow diagrams --------------------------------- Each item describes one operation box. Apply its rule exactly as stated. 1. diagrammatic-reasoning-s01-q01 --------------------------------- A flow diagram shows a single box labelled 'Add 4'. The number 9 enters the box. What number comes out? - A. 5 - B. 12 - C. 13 - D. 36 Your answer: ______ 2. diagrammatic-reasoning-s01-q02 --------------------------------- A box labelled 'Double' receives the number 7. What is the output? - A. 9 - B. 14 - C. 21 - D. 49 Your answer: ______ 3. diagrammatic-reasoning-s01-q03 --------------------------------- A box labelled 'Reverse' receives the letter sequence P-Q-R. What sequence comes out? - A. P-Q-R - B. Q-P-R - C. R-Q-P - D. R-P-Q Your answer: ______ 4. diagrammatic-reasoning-s01-q04 --------------------------------- A box labelled 'Remove the last item' receives the list: apple, pear, plum. What list comes out? - A. apple, pear - B. pear, plum - C. apple, plum - D. apple, pear, plum Your answer: ______ 5. diagrammatic-reasoning-s01-q05 --------------------------------- A box labelled 'Rotate 90° clockwise' receives a printed arrow pointing straight up. Which way does the arrow point on the way out? - A. Up - B. Down - C. Left - D. Right Your answer: ______ 6. diagrammatic-reasoning-s01-q06 --------------------------------- A box labelled 'Swap the first and last symbols' receives the sequence ★ ● ▲ ■. What comes out? - A. ■ ● ▲ ★ - B. ● ★ ■ ▲ - C. ■ ▲ ● ★ - D. ★ ■ ▲ ● Your answer: ______ 7. diagrammatic-reasoning-s01-q07 --------------------------------- A box labelled 'Halve' receives the number 26. What is the output? - A. 12 - B. 13 - C. 24 - D. 52 Your answer: ______ 8. diagrammatic-reasoning-s01-q08 --------------------------------- A box labelled 'Toggle shading' turns white figures black and black figures white without changing the shape. A white triangle enters. What comes out? - A. A white triangle - B. A black square - C. A white circle - D. A black triangle Your answer: ______ 9. diagrammatic-reasoning-s01-q09 --------------------------------- A box labelled 'Repeat the whole sequence twice' receives the sequence A-B. What comes out? - A. A-A-B-B - B. A-B-A-B - C. A-B-B-A - D. B-A-B-A Your answer: ______ 10. diagrammatic-reasoning-s01-q10 ---------------------------------- A box labelled 'Subtract 6' receives the number 6. What is the output? - A. 0 - B. 1 - C. 6 - D. 12 Your answer: ______ Two-step operator chains ------------------------ Apply the two boxes strictly in the order shown, left to right. 11. diagrammatic-reasoning-s02-q01 ---------------------------------- The number 5 enters [Add 3] and the result enters [Double]. What is the output? - A. 13 - B. 16 - C. 11 - D. 10 Your answer: ______ 12. diagrammatic-reasoning-s02-q02 ---------------------------------- The number 12 enters [Halve] and the result enters [Subtract 2]. What is the output? - A. 4 - B. 5 - C. 8 - D. 10 Your answer: ______ 13. diagrammatic-reasoning-s02-q03 ---------------------------------- The letters C-A-T enter [Reverse] and the result enters [Remove the last letter]. What comes out? - A. A-T - B. C-A - C. T-C - D. T-A Your answer: ______ 14. diagrammatic-reasoning-s02-q04 ---------------------------------- An arrow pointing north enters [Rotate 90° clockwise] and the result enters [Rotate 180°]. Which way does it finally point? - A. North - B. East - C. West - D. South Your answer: ______ 15. diagrammatic-reasoning-s02-q05 ---------------------------------- The list 2, 4, 6, 8 enters [Remove the first item] and the result enters [Reverse]. What comes out? - A. 8, 6, 4, 2 - B. 8, 6, 4 - C. 4, 6, 8 - D. 6, 4, 2 Your answer: ______ 16. diagrammatic-reasoning-s02-q06 ---------------------------------- The number 3 enters [Square] and the result enters [Add 1]. What is the output? - A. 16 - B. 7 - C. 9 - D. 10 Your answer: ______ 17. diagrammatic-reasoning-s02-q07 ---------------------------------- A white circle enters [Toggle shading] and the result enters [Rotate 90° clockwise]. What comes out? - A. A black circle - B. A white circle - C. A black square - D. A white square Your answer: ______ 18. diagrammatic-reasoning-s02-q08 ---------------------------------- The word STAR enters [Swap the first and last letters] and the result enters [Reverse]. What comes out? - A. RATS - B. RTAS - C. SATR - D. TARS Your answer: ______ 19. diagrammatic-reasoning-s02-q09 ---------------------------------- The number 18 enters [Subtract 4] and the result enters [Halve]. What is the output? - A. 9 - B. 5 - C. 7 - D. 14 Your answer: ______ 20. diagrammatic-reasoning-s02-q10 ---------------------------------- 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? - A. 16 - B. 14 - C. 12 - D. 10 Your answer: ______ Inferring hidden rules from examples ------------------------------------ Each box's rule is unknown: deduce it from the example pairs by testing every candidate against every pair. 21. diagrammatic-reasoning-s03-q01 ---------------------------------- A mystery box turns 3 into 6, 5 into 10, and 9 into 18. What is the box's rule? - A. It adds 3 - B. It doubles - C. It squares - D. It adds 5 Your answer: ______ 22. diagrammatic-reasoning-s03-q02 ---------------------------------- A mystery box turns 10 into 7, 8 into 5, and 6 into 3. What is its rule? - A. It halves - B. It subtracts 2 - C. It subtracts 4 - D. It subtracts 3 Your answer: ______ 23. diagrammatic-reasoning-s03-q03 ---------------------------------- A mystery box turns CAT into TAC and STOP into POTS. What is its rule? - A. It reverses all the letters - B. It swaps only the first and last letters - C. It moves the last letter to the front - D. It writes the letters in alphabetical order Your answer: ______ 24. diagrammatic-reasoning-s03-q04 ---------------------------------- A mystery box turns 4 into 16, 5 into 25, and 7 into 49. What is its rule? - A. It multiplies by 4 - B. It adds 12 - C. It squares - D. It multiplies by 5 Your answer: ______ 25. diagrammatic-reasoning-s03-q05 ---------------------------------- 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? - A. It repeats the whole sequence - B. It copies the first symbol onto the end - C. It copies the last symbol onto the front - D. It reverses the sequence Your answer: ______ 26. diagrammatic-reasoning-s03-q06 ---------------------------------- A mystery box turns 7 into 15, 10 into 21, and 4 into 9. What is its rule? - A. It doubles, then adds 1 - B. It adds 8 - C. It doubles, then subtracts 1 - D. It triples, then subtracts 6 Your answer: ______ 27. diagrammatic-reasoning-s03-q07 ---------------------------------- A mystery box turns a black square into a white square, and a white triangle into a black triangle. What is its rule? - A. It turns every figure black - B. It turns every figure white - C. It changes the shape but keeps the shading - D. It swaps the shading but keeps the shape Your answer: ______ 28. diagrammatic-reasoning-s03-q08 ---------------------------------- A mystery box turns 12 into 6, 20 into 10, and 8 into 4. What is its rule? - A. It subtracts 6 - B. It subtracts 10 - C. It halves - D. It divides by 3 Your answer: ______ 29. diagrammatic-reasoning-s03-q09 ---------------------------------- A mystery box turns BOLT into BOL, RAIN into RAI, and TREE into TRE. What is its rule? - A. It removes the last letter - B. It removes the first letter - C. It keeps only the first letter - D. It removes all vowels Your answer: ______ 30. diagrammatic-reasoning-s03-q10 ---------------------------------- A mystery box turns 2 into 8. Which rule is consistent with BOTH 2→8 and 3→27? - A. It multiplies by 4 - B. It cubes - C. It adds 6 - D. It squares, then adds 4 Your answer: ______ Sequence and series patterns ---------------------------- Work out the pattern that generates each series, then predict the next term. 31. diagrammatic-reasoning-s04-q01 ---------------------------------- A series of frames shows: 1 dot, 2 dots, 3 dots, 4 dots. How many dots are in the next frame? - A. 4 dots - B. 6 dots - C. 3 dots - D. 5 dots Your answer: ______ 32. diagrammatic-reasoning-s04-q02 ---------------------------------- A series of squares alternates: black, white, black, white. What colour is the next square? - A. Black - B. White - C. Grey - D. Striped Your answer: ______ 33. diagrammatic-reasoning-s04-q03 ---------------------------------- An arrow rotates the same amount each frame: it points up, then right, then down. Where does it point next? - A. Up - B. Right - C. Left - D. Down Your answer: ______ 34. diagrammatic-reasoning-s04-q04 ---------------------------------- 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? - A. 5 white dots - B. 5 black dots - C. 4 black dots - D. 6 white dots Your answer: ______ 35. diagrammatic-reasoning-s04-q05 ---------------------------------- A series of shapes shows: triangle, square, pentagon. Which shape comes next? - A. Circle - B. Triangle - C. Octagon - D. Hexagon Your answer: ______ 36. diagrammatic-reasoning-s04-q06 ---------------------------------- 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? - A. Top-left corner - B. Bottom-left corner - C. Top-right corner - D. The centre Your answer: ______ 37. diagrammatic-reasoning-s04-q07 ---------------------------------- What is the next number in the series: 2, 4, 3, 6, 5, 10, 9, ...? - A. 18 - B. 11 - C. 8 - D. 13 Your answer: ______ 38. diagrammatic-reasoning-s04-q08 ---------------------------------- What is the next letter in the series: A, C, F, J, ...? - A. N - B. M - C. O - D. P Your answer: ______ 39. diagrammatic-reasoning-s04-q09 ---------------------------------- 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? - A. A large arrow pointing left - B. A medium arrow pointing left - C. A small arrow pointing up - D. A small arrow pointing left Your answer: ______ 40. diagrammatic-reasoning-s04-q10 ---------------------------------- 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? - A. 4 - B. 6 - C. 5 - D. 7 Your answer: ______ Branching flowcharts and decisions ---------------------------------- Follow each decision diamond carefully. Answer the question asked at each branch before moving on. 41. diagrammatic-reasoning-s05-q01 ---------------------------------- 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? - A. 8 - B. 7 - C. 10 - D. 11 Your answer: ______ 42. diagrammatic-reasoning-s05-q02 ---------------------------------- 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? - A. 6 - B. 24 - C. 12 - D. 5 Your answer: ______ 43. diagrammatic-reasoning-s05-q03 ---------------------------------- 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? - A. 15 - B. 5 - C. 10 - D. 4 Your answer: ______ 44. diagrammatic-reasoning-s05-q04 ---------------------------------- 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? - A. ORANG - B. EGNARO - C. ORANGE - D. GNARO Your answer: ______ 45. diagrammatic-reasoning-s05-q05 ---------------------------------- 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? - A. 6 - B. 5 - C. 18 - D. 9 Your answer: ______ 46. diagrammatic-reasoning-s05-q06 ---------------------------------- 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? - A. Depot A - B. Depot B - C. Depot C - D. It cannot be determined Your answer: ______ 47. diagrammatic-reasoning-s05-q07 ---------------------------------- Using the same sorting chart, over 2 kg → Depot B; otherwise fragile → Depot C; otherwise → Depot A, which parcel ends up at Depot A? - A. A 3 kg parcel, not fragile - B. A 1 kg parcel, marked fragile - C. A 2.5 kg parcel, marked fragile - D. A 1.8 kg parcel, not fragile Your answer: ______ 48. diagrammatic-reasoning-s05-q08 ---------------------------------- 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? - A. 4 - B. 14 - C. 12 - D. 24 Your answer: ______ 49. diagrammatic-reasoning-s05-q09 ---------------------------------- A flowchart doubles even inputs and adds 5 to odd inputs. The output was 18. What was the input? - A. 9 - B. 13 - C. 36 - D. 23 Your answer: ______ 50. diagrammatic-reasoning-s05-q10 ---------------------------------- 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? - A. 3 - B. 6 - C. 9 - D. 15 Your answer: ______ State and process diagrams -------------------------- Track the current state after each signal. States change only when a listed transition allows it. 51. diagrammatic-reasoning-s06-q01 ---------------------------------- A traffic system cycles Green → Amber → Red → Green, one step per change. It currently shows Amber. What does it show after two changes? - A. Green - B. Red - C. Amber - D. Flashing amber Your answer: ______ 52. diagrammatic-reasoning-s06-q02 ---------------------------------- 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? - A. Locked - B. Closed - C. Open - D. It cannot be determined Your answer: ______ 53. diagrammatic-reasoning-s06-q03 ---------------------------------- 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? - A. Idle - B. Ready - C. Refunding - D. Printing Your answer: ______ 54. diagrammatic-reasoning-s06-q04 ---------------------------------- The same ticket machine ignores a button press while Idle. From Idle, the sequence is: press button, insert coin, press button. What state results? - A. Idle - B. Printing - C. Ready - D. The machine jams Your answer: ______ 55. diagrammatic-reasoning-s06-q05 ---------------------------------- 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? - A. Floor 3 - B. Floor 5 - C. Floor 4 - D. Floor 2 Your answer: ______ 56. diagrammatic-reasoning-s06-q06 ---------------------------------- 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? - A. Spin - B. Rinse - C. Wash - D. Done Your answer: ______ 57. diagrammatic-reasoning-s06-q07 ---------------------------------- 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? - A. Unlocked - B. Locked - C. Jammed - D. It cannot be determined Your answer: ______ 58. diagrammatic-reasoning-s06-q08 ---------------------------------- 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? - A. Stations 1 and 2 - B. Station 2 only - C. Stations 1, 2 and 3 - D. Stations 1 and 3 Your answer: ______ 59. diagrammatic-reasoning-s06-q09 ---------------------------------- 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? - A. Fresh - B. Tired - C. Exhausted - D. It cannot be determined Your answer: ______ 60. diagrammatic-reasoning-s06-q10 ---------------------------------- 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? - A. 0p - B. 10p - C. 20p - D. 30p Your answer: ______ Deducing unknown operators in pipelines --------------------------------------- Work out what each mystery operator does from its examples before applying it to the new input. 61. diagrammatic-reasoning-s07-q01 ---------------------------------- Operator ◆ turns 4 into 8 and 10 into 20. What does ◆ give for the input 6? - A. 10 - B. 12 - C. 8 - D. 36 Your answer: ______ 62. diagrammatic-reasoning-s07-q02 ---------------------------------- Operator ● turns A-B-C into C-B-A and P-Q into Q-P. What does ● give for R-S-T? - A. R-S-T - B. S-R-T - C. R-T-S - D. T-S-R Your answer: ______ 63. diagrammatic-reasoning-s07-q03 ---------------------------------- Operator ◆ doubles its input. Operator ● turns 5 into 8 and 9 into 12. What is the output of 4 → [◆] → [●]? - A. 11 - B. 14 - C. 10 - D. 19 Your answer: ______ 64. diagrammatic-reasoning-s07-q04 ---------------------------------- Operator ▲ turns 1-2-3 into 2-3, and 7-8-9-10 into 8-9-10. What does ▲ give for X-Y-Z? - A. X-Y - B. Z - C. Y-Z - D. X-Z Your answer: ______ 65. diagrammatic-reasoning-s07-q05 ---------------------------------- A single mystery box turns 3 into 9 and 5 into 15. What is its rule? - A. It squares - B. It adds 6 - C. It multiplies by 3 - D. It adds 10 Your answer: ______ 66. diagrammatic-reasoning-s07-q06 ---------------------------------- 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? - A. Add 3 - B. Double - C. Subtract 5 - D. Add 5 Your answer: ______ 67. diagrammatic-reasoning-s07-q07 ---------------------------------- Operator ■ toggles shading (white ↔ black). Operator ▲ rotates a figure 90° clockwise. A white arrow pointing up passes through [▲] then [■]. What comes out? - A. A white arrow pointing right - B. A black arrow pointing right - C. A black arrow pointing up - D. A black arrow pointing left Your answer: ______ 68. diagrammatic-reasoning-s07-q08 ---------------------------------- 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? - A. Halve first, then Add 2 - B. Add 2 first, then Halve - C. Either order gives 5 - D. Neither order can give 5 Your answer: ______ 69. diagrammatic-reasoning-s07-q09 ---------------------------------- In the pipeline input → [Reverse] → [◇] → output, the input 4-7-2 produces 2-7 and the input 1-5 produces 5. What does ◇ do? - A. It removes the first item - B. It keeps only the first item - C. It reverses again - D. It removes the last item Your answer: ______ 70. diagrammatic-reasoning-s07-q10 ---------------------------------- In the pipeline 5 → [Double] → [X] → [Double] → 14, operator X applies the same rule every time. What does X give for the input 12? - A. 9 - B. 15 - C. 24 - D. 6 Your answer: ______ Loops and repeated processes ---------------------------- Repeat the rule exactly as stated and re-check the stopping condition after every pass. 71. diagrammatic-reasoning-s08-q01 ---------------------------------- Start with 3. Keep doubling until the number exceeds 20, then stop. What is the final number? - A. 12 - B. 20 - C. 48 - D. 24 Your answer: ______ 72. diagrammatic-reasoning-s08-q02 ---------------------------------- Start with 2. Keep doubling until the number exceeds 30. How many doublings are performed? - A. 5 - B. 4 - C. 3 - D. 6 Your answer: ______ 73. diagrammatic-reasoning-s08-q03 ---------------------------------- Start with 100. Repeatedly subtract 15 until the result is 40 or less. What is the final number? - A. 40 - B. 25 - C. 55 - D. 45 Your answer: ______ 74. diagrammatic-reasoning-s08-q04 ---------------------------------- Start with 1. Add 3 on each pass and stop as soon as the total reaches 13 or more. How many passes run? - A. 3 - B. 5 - C. 4 - D. 6 Your answer: ______ 75. diagrammatic-reasoning-s08-q05 ---------------------------------- Start with the word DIAGRAMS. Remove the last letter repeatedly until exactly 4 letters remain. What is left? - A. DIAG - B. DIAGR - C. RAMS - D. DIA Your answer: ______ 76. diagrammatic-reasoning-s08-q06 ---------------------------------- 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? - A. 7 - B. 14 - C. 6 - D. 12 Your answer: ______ 77. diagrammatic-reasoning-s08-q07 ---------------------------------- Start with 5. On odd-numbered passes (1st, 3rd, ...) add 2; on even-numbered passes subtract 1. Run exactly 4 passes. What results? - A. 9 - B. 6 - C. 7 - D. 8 Your answer: ______ 78. diagrammatic-reasoning-s08-q08 ---------------------------------- A loop halves the number while it is even. Start with 48. What is the final number? - A. 6 - B. 3 - C. 1 - D. 24 Your answer: ______ 79. diagrammatic-reasoning-s08-q09 ---------------------------------- 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? - A. 4 - B. 5 - C. 2 - D. 8 Your answer: ______ 80. diagrammatic-reasoning-s08-q10 ---------------------------------- A loop applies this rule: if the number is odd, add 2; stop when the number becomes even. Start with 9. What happens? - A. It stops at 10 - B. It stops at 11 - C. It stops after exactly five passes - D. It never stops Your answer: ______ Fault-finding in operator networks ---------------------------------- A box may fail by passing its input through unchanged. Compare expected and actual outputs to isolate the fault. 81. diagrammatic-reasoning-s09-q01 ---------------------------------- 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? - A. The Add 5 box - B. The Double box - C. Both boxes - D. Neither box Your answer: ______ 82. diagrammatic-reasoning-s09-q02 ---------------------------------- 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? - A. The Reverse box - B. The Remove box - C. Both boxes - D. Neither box Your answer: ______ 83. diagrammatic-reasoning-s09-q03 ---------------------------------- 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? - A. The Triple box - B. Both boxes - C. The Subtract 2 box - D. Neither box Your answer: ______ 84. diagrammatic-reasoning-s09-q04 ---------------------------------- 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? - A. The Rotate box - B. Both boxes - C. Neither box - D. The Toggle shading box Your answer: ______ 85. diagrammatic-reasoning-s09-q05 ---------------------------------- 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? - A. The Add 1 box - B. The Double box - C. The Subtract 3 box - D. It cannot be determined Your answer: ______ 86. diagrammatic-reasoning-s09-q06 ---------------------------------- 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? - A. The first Double box - B. The second Double box - C. The Subtract 4 box - D. None of the boxes Your answer: ______ 87. diagrammatic-reasoning-s09-q07 ---------------------------------- A box labelled 'Add 10' receives 7 and outputs 27. Which fault mode best describes its behaviour? - A. It did nothing - B. It applied its rule twice - C. It subtracted instead of adding - D. It worked correctly Your answer: ______ 88. diagrammatic-reasoning-s09-q08 ---------------------------------- 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? - A. The Subtract 8 box - B. Both boxes - C. Neither box - D. The Halve box Your answer: ______ 89. diagrammatic-reasoning-s09-q09 ---------------------------------- 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? - A. The Reverse box - B. The second Remove box - C. None of the boxes - D. The first Remove box Your answer: ______ 90. diagrammatic-reasoning-s09-q10 ---------------------------------- 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? - A. It doubled correctly in the first test but passed the input unchanged in the second - B. It always works correctly - C. It never works correctly - D. It halves even numbers Your answer: ______ Integrated system challenges ---------------------------- These combine rule deduction, ordering, loops, and faults. Verify each stage before moving to the next. 91. diagrammatic-reasoning-s10-q01 ---------------------------------- A white arrow pointing north passes through [Rotate 90° clockwise] → [Toggle shading] → [Rotate 90° clockwise]. What comes out? - A. A white arrow pointing south - B. A black arrow pointing north - C. A black arrow pointing south - D. A black arrow pointing west Your answer: ______ 92. diagrammatic-reasoning-s10-q02 ---------------------------------- 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? - A. 19 - B. 16 - C. 13 - D. 22 Your answer: ______ 93. diagrammatic-reasoning-s10-q03 ---------------------------------- 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? - A. 19 - B. 11 - C. 60 - D. 7 Your answer: ______ 94. diagrammatic-reasoning-s10-q04 ---------------------------------- 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? - A. 64 - B. 8 - C. 16 - D. 32 Your answer: ______ 95. diagrammatic-reasoning-s10-q05 ---------------------------------- Analogy: a white arrow pointing up is to a white arrow pointing right as a black arrow pointing left is to what? - A. A black arrow pointing down - B. A white arrow pointing up - C. A black arrow pointing right - D. A black arrow pointing up Your answer: ______ 96. diagrammatic-reasoning-s10-q06 ---------------------------------- 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? - A. 23 - B. 21 - C. 19 - D. 20 Your answer: ______ 97. diagrammatic-reasoning-s10-q07 ---------------------------------- 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? - A. 23 - B. 11 - C. 22 - D. 21 Your answer: ______ 98. diagrammatic-reasoning-s10-q08 ---------------------------------- 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? - A. 7 - B. 8 - C. 6 - D. 9 Your answer: ______ 99. diagrammatic-reasoning-s10-q09 ---------------------------------- 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? - A. 7 - B. 6 - C. 5 - D. 9 Your answer: ______ 100. diagrammatic-reasoning-s10-q10 ----------------------------------- 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? - A. 12 - B. 9 - C. 18 - D. 6 Your answer: ______ Authored hints ============== 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. 100 worksheet items do not have an authored hint. No hint text was generated for them. Answer key ========== ! The answer key and worked explanations in this file belong only to this public, untimed educational practice source. No active aptitude suite or Novus Reasoning Challenge answer key is ever included in any download. Diagrammatic reasoning: transformations, flows, and rule diagrams: open practice pack answer key Item Choice Answer ------------------------------ ------ ----------------------------------------------------------------------------------- diagrammatic-reasoning-s01-q01 C 13 diagrammatic-reasoning-s01-q02 B 14 diagrammatic-reasoning-s01-q03 C R-Q-P diagrammatic-reasoning-s01-q04 A apple, pear diagrammatic-reasoning-s01-q05 D Right diagrammatic-reasoning-s01-q06 A ■ ● ▲ ★ diagrammatic-reasoning-s01-q07 B 13 diagrammatic-reasoning-s01-q08 D A black triangle diagrammatic-reasoning-s01-q09 B A-B-A-B diagrammatic-reasoning-s01-q10 A 0 diagrammatic-reasoning-s02-q01 B 16 diagrammatic-reasoning-s02-q02 A 4 diagrammatic-reasoning-s02-q03 D T-A diagrammatic-reasoning-s02-q04 C West diagrammatic-reasoning-s02-q05 B 8, 6, 4 diagrammatic-reasoning-s02-q06 D 10 diagrammatic-reasoning-s02-q07 A A black circle diagrammatic-reasoning-s02-q08 C SATR diagrammatic-reasoning-s02-q09 C 7 diagrammatic-reasoning-s02-q10 B 14 diagrammatic-reasoning-s03-q01 B It doubles diagrammatic-reasoning-s03-q02 D It subtracts 3 diagrammatic-reasoning-s03-q03 A It reverses all the letters diagrammatic-reasoning-s03-q04 C It squares diagrammatic-reasoning-s03-q05 B It copies the first symbol onto the end diagrammatic-reasoning-s03-q06 A It doubles, then adds 1 diagrammatic-reasoning-s03-q07 D It swaps the shading but keeps the shape diagrammatic-reasoning-s03-q08 C It halves diagrammatic-reasoning-s03-q09 A It removes the last letter diagrammatic-reasoning-s03-q10 B It cubes diagrammatic-reasoning-s04-q01 D 5 dots diagrammatic-reasoning-s04-q02 A Black diagrammatic-reasoning-s04-q03 C Left diagrammatic-reasoning-s04-q04 B 5 black dots diagrammatic-reasoning-s04-q05 D Hexagon diagrammatic-reasoning-s04-q06 B Bottom-left corner diagrammatic-reasoning-s04-q07 A 18 diagrammatic-reasoning-s04-q08 C O diagrammatic-reasoning-s04-q09 D A small arrow pointing left diagrammatic-reasoning-s04-q10 C 5 diagrammatic-reasoning-s05-q01 C 10 diagrammatic-reasoning-s05-q02 A 6 diagrammatic-reasoning-s05-q03 B 5 diagrammatic-reasoning-s05-q04 D GNARO diagrammatic-reasoning-s05-q05 A 6 diagrammatic-reasoning-s05-q06 C Depot C diagrammatic-reasoning-s05-q07 D A 1.8 kg parcel, not fragile diagrammatic-reasoning-s05-q08 B 14 diagrammatic-reasoning-s05-q09 B 13 diagrammatic-reasoning-s05-q10 D 15 diagrammatic-reasoning-s06-q01 A Green diagrammatic-reasoning-s06-q02 C Open diagrammatic-reasoning-s06-q03 D Printing diagrammatic-reasoning-s06-q04 B Printing diagrammatic-reasoning-s06-q05 C Floor 4 diagrammatic-reasoning-s06-q06 A Spin diagrammatic-reasoning-s06-q07 B Locked diagrammatic-reasoning-s06-q08 D Stations 1 and 3 diagrammatic-reasoning-s06-q09 A Fresh diagrammatic-reasoning-s06-q10 C 20p diagrammatic-reasoning-s07-q01 B 12 diagrammatic-reasoning-s07-q02 D T-S-R diagrammatic-reasoning-s07-q03 A 11 diagrammatic-reasoning-s07-q04 C Y-Z diagrammatic-reasoning-s07-q05 C It multiplies by 3 diagrammatic-reasoning-s07-q06 D Add 5 diagrammatic-reasoning-s07-q07 B A black arrow pointing right diagrammatic-reasoning-s07-q08 A Halve first, then Add 2 diagrammatic-reasoning-s07-q09 D It removes the last item diagrammatic-reasoning-s07-q10 A 9 diagrammatic-reasoning-s08-q01 D 24 diagrammatic-reasoning-s08-q02 B 4 diagrammatic-reasoning-s08-q03 A 40 diagrammatic-reasoning-s08-q04 C 4 diagrammatic-reasoning-s08-q05 A DIAG diagrammatic-reasoning-s08-q06 D 12 diagrammatic-reasoning-s08-q07 C 7 diagrammatic-reasoning-s08-q08 B 3 diagrammatic-reasoning-s08-q09 A 4 diagrammatic-reasoning-s08-q10 D It never stops diagrammatic-reasoning-s09-q01 B The Double box diagrammatic-reasoning-s09-q02 A The Reverse box diagrammatic-reasoning-s09-q03 C The Subtract 2 box diagrammatic-reasoning-s09-q04 D The Toggle shading box diagrammatic-reasoning-s09-q05 A The Add 1 box diagrammatic-reasoning-s09-q06 C The Subtract 4 box diagrammatic-reasoning-s09-q07 B It applied its rule twice diagrammatic-reasoning-s09-q08 D The Halve box diagrammatic-reasoning-s09-q09 D The first Remove box diagrammatic-reasoning-s09-q10 A It doubled correctly in the first test but passed the input unchanged in the second diagrammatic-reasoning-s10-q01 C A black arrow pointing south diagrammatic-reasoning-s10-q02 D 22 diagrammatic-reasoning-s10-q03 B 11 diagrammatic-reasoning-s10-q04 A 64 diagrammatic-reasoning-s10-q05 D A black arrow pointing up diagrammatic-reasoning-s10-q06 C 19 diagrammatic-reasoning-s10-q07 A 23 diagrammatic-reasoning-s10-q08 B 8 diagrammatic-reasoning-s10-q09 C 5 diagrammatic-reasoning-s10-q10 B 9 Worked explanations =================== diagrammatic-reasoning-s01-q01 An 'Add 4' box outputs its input plus 4, so 9 becomes 9 + 4 = 13. diagrammatic-reasoning-s01-q02 Doubling multiplies the input by 2, so 7 becomes 14. diagrammatic-reasoning-s01-q03 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. diagrammatic-reasoning-s01-q04 The box deletes only the final item (plum), leaving the rest in their original order. diagrammatic-reasoning-s01-q05 A quarter turn clockwise moves an upward arrow to point right, imagine turning a clock hand from 12 to 3. diagrammatic-reasoning-s01-q06 Only the two end symbols trade places (★ and ■); the middle symbols stay exactly where they were. diagrammatic-reasoning-s01-q07 Halving divides the input by 2, so 26 becomes 13. diagrammatic-reasoning-s01-q08 The box changes shading only, so the triangle keeps its shape but flips from white to black. diagrammatic-reasoning-s01-q09 Repeating the whole sequence writes the complete run again after itself, giving A-B followed by A-B, not each symbol doubled in place. diagrammatic-reasoning-s01-q10 6 − 6 = 0, a valid output; an operator can produce zero. diagrammatic-reasoning-s02-q01 Work left to right: 5 + 3 = 8, then 8 × 2 = 16. diagrammatic-reasoning-s02-q02 12 ÷ 2 = 6, then 6 − 2 = 4. diagrammatic-reasoning-s02-q03 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. diagrammatic-reasoning-s02-q04 North turned 90° clockwise points east; a further 180° turn points it the opposite way, west. diagrammatic-reasoning-s02-q05 Removing the first item leaves 4, 6, 8; reversing that gives 8, 6, 4. diagrammatic-reasoning-s02-q06 3 squared is 9, and 9 + 1 = 10. diagrammatic-reasoning-s02-q07 Toggling makes the circle black, and rotating a circle produces no visible change. Some operators have no effect on symmetric figures. diagrammatic-reasoning-s02-q08 Swapping the end letters of STAR gives RTAS; reversing RTAS gives SATR. Track the intermediate result carefully at each stage. diagrammatic-reasoning-s02-q09 18 − 4 = 14, then 14 ÷ 2 = 7. diagrammatic-reasoning-s02-q10 Order matters in a pipeline: doubling first gives 12, then adding 2 gives 14, a different result from the original wiring. diagrammatic-reasoning-s03-q01 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. diagrammatic-reasoning-s03-q02 Halving fits 6→3 but fails 10→7; subtracting 3 is the only rule that fits every pair. diagrammatic-reasoning-s03-q03 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. diagrammatic-reasoning-s03-q04 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. diagrammatic-reasoning-s03-q05 In both examples the output is the original sequence with its opening symbol appended at the end, nothing else moves. diagrammatic-reasoning-s03-q06 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. diagrammatic-reasoning-s03-q07 Both examples keep their shape while black and white exchange, so the rule acts on shading alone. diagrammatic-reasoning-s03-q08 Subtracting 6 fits 12→6 but fails 20→10; each output is exactly half its input, so the box halves. diagrammatic-reasoning-s03-q09 Every output is the input with just its final letter missing: removing vowels would have turned RAIN into RN. diagrammatic-reasoning-s03-q10 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. diagrammatic-reasoning-s04-q01 The count rises by one dot per frame, so the next frame shows 5 dots. diagrammatic-reasoning-s04-q02 The shading alternates every frame, and the last square shown was white, so black follows. diagrammatic-reasoning-s04-q03 Each frame turns the arrow 90° clockwise (up → right → down), so the next quarter turn points it left. diagrammatic-reasoning-s04-q04 Two features change independently: the count rises by one each frame while the shading alternates. After 4 white comes 5 black. diagrammatic-reasoning-s04-q05 Each shape has one more side than the last (3, 4, 5), so a six-sided hexagon comes next. diagrammatic-reasoning-s04-q06 The star moves one corner clockwise each frame, so from bottom-right it reaches bottom-left. diagrammatic-reasoning-s04-q07 Two rules alternate: double, then subtract 1 (2→4→3→6→5→10→9). The next step doubles again: 9 × 2 = 18. diagrammatic-reasoning-s04-q08 The gaps grow by one each step: +2, +3, +4, so the next gap is +5. Five letters past J is O. diagrammatic-reasoning-s04-q09 Track each feature separately: the size cycle returns to small, while the rotation continues from down to left. diagrammatic-reasoning-s04-q10 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. diagrammatic-reasoning-s05-q01 7 is odd, so the No branch applies: 7 + 3 = 10. diagrammatic-reasoning-s05-q02 12 is greater than 10, so it is halved to 6. diagrammatic-reasoning-s05-q03 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. diagrammatic-reasoning-s05-q04 ORANGE has 6 letters, so it becomes ORANG; ORANG starts with the vowel O, so it is reversed to GNARO. diagrammatic-reasoning-s05-q05 15 is a multiple of 3, giving 5; 5 is odd, so adding 1 gives 6. diagrammatic-reasoning-s05-q06 At 1.5 kg the parcel passes the weight test, so the fragile question decides: fragile parcels go to Depot C. diagrammatic-reasoning-s05-q07 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. diagrammatic-reasoning-s05-q08 24 halves to 12; 12 divides by 3 to give 4; 4 is not greater than 5, so adding 10 gives 14. diagrammatic-reasoning-s05-q09 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. diagrammatic-reasoning-s05-q10 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. diagrammatic-reasoning-s06-q01 From Amber, one change reaches Red and a second completes the cycle to Green. diagrammatic-reasoning-s06-q02 Turning the key moves Locked to Closed, and pushing then opens the door. diagrammatic-reasoning-s06-q03 The coin moves the machine to Ready and the button press moves it on to Printing. diagrammatic-reasoning-s06-q04 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. diagrammatic-reasoning-s06-q05 Trace floor by floor: 2 → 3 → 4 → 3 → 4. diagrammatic-reasoning-s06-q06 Fill advances to Wash, then Rinse; the hold keeps it at Rinse; the final advance reaches Spin. diagrammatic-reasoning-s06-q07 The first coin unlocks it, the second coin is ignored, the first push relocks it, and the second push is ignored, ending Locked. diagrammatic-reasoning-s06-q08 Every crate passes through Station 1 first; crate 8 is even, so it is routed on to Station 3 and never sees Station 2. diagrammatic-reasoning-s06-q09 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. diagrammatic-reasoning-s06-q10 The second 20p lifts credit to 40p, triggering a vend that leaves 10p; the final 10p brings credit to 20p, below the vend threshold. diagrammatic-reasoning-s07-q01 Both examples double their input, so ◆ turns 6 into 12. diagrammatic-reasoning-s07-q02 Both examples reverse the sequence, so R-S-T becomes T-S-R. diagrammatic-reasoning-s07-q03 ● adds 3 in both examples, so the pipeline gives 4 × 2 = 8, then 8 + 3 = 11. diagrammatic-reasoning-s07-q04 In both examples only the first item disappears, so ▲ removes the opening item and X-Y-Z becomes Y-Z. diagrammatic-reasoning-s07-q05 Squaring fits 3→9 but fails 5→15, and adding 6 fails 5→15 too, only multiplying by 3 fits both examples. diagrammatic-reasoning-s07-q06 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. diagrammatic-reasoning-s07-q07 The rotation turns the arrow to point right, and the toggle then flips it from white to black. diagrammatic-reasoning-s07-q08 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. diagrammatic-reasoning-s07-q09 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. diagrammatic-reasoning-s07-q10 Work backwards: the final Double must have received 7, so X turned 10 into 7: it subtracts 3, turning 12 into 9. diagrammatic-reasoning-s08-q01 3 → 6 → 12 → 24; 24 is the first value over 20, and the loop stops there rather than doubling again. diagrammatic-reasoning-s08-q02 2 → 4 → 8 → 16 → 32, four doublings bring the number past 30. diagrammatic-reasoning-s08-q03 100 → 85 → 70 → 55 → 40; the condition '40 or less' is met exactly at 40, so no further pass runs. diagrammatic-reasoning-s08-q04 1 → 4 → 7 → 10 → 13: four additions reach the threshold exactly. diagrammatic-reasoning-s08-q05 DIAGRAMS has 8 letters, so four removals from the end leave the first four: DIAG. diagrammatic-reasoning-s08-q06 9 is odd → 14; 14 is even → 7; 7 is odd → 12. Re-test the even/odd condition on each new value. diagrammatic-reasoning-s08-q07 Track the pass number separately from the value: 5 → 7 → 6 → 8 → 7 after passes 1 to 4. diagrammatic-reasoning-s08-q08 48 → 24 → 12 → 6 → 3; the loop stops at 3 because the condition 'while even' finally fails. diagrammatic-reasoning-s08-q09 7 → 10 → 5 → 8 → 4. Note that 5 is not below 5, so the loop must continue past it. Read stopping conditions literally. diagrammatic-reasoning-s08-q10 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. diagrammatic-reasoning-s09-q01 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. diagrammatic-reasoning-s09-q02 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. diagrammatic-reasoning-s09-q03 With Subtract 2 broken, the Triple box receives 6 unchanged and outputs 18, matching the observation. A broken Triple box would have given 4. diagrammatic-reasoning-s09-q04 The rotation clearly happened (the arrow points down), but the shading never flipped, so the toggle box passed its input through untouched. diagrammatic-reasoning-s09-q05 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. diagrammatic-reasoning-s09-q06 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. diagrammatic-reasoning-s09-q07 Correct behaviour would give 17 and doing nothing would give 7; the observed 27 equals 7 + 10 + 10, the rule applied twice over. diagrammatic-reasoning-s09-q08 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. diagrammatic-reasoning-s09-q09 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. diagrammatic-reasoning-s09-q10 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. diagrammatic-reasoning-s10-q01 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. diagrammatic-reasoning-s10-q02 From the examples, ● adds 3 (12 → 15 and 20 → 23). Reversing the order changes the result: 8 + 3 = 11, then doubled to 22. diagrammatic-reasoning-s10-q03 3 × 5 = 15, and the difference between 15 and 4 is 11. diagrammatic-reasoning-s10-q04 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. diagrammatic-reasoning-s10-q05 The first pair shows a 90° clockwise rotation with shading preserved; rotating a left-pointing arrow 90° clockwise points it up, still black. diagrammatic-reasoning-s10-q06 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. diagrammatic-reasoning-s10-q07 Each full pass maps n to 2n + 1: 2 → 5 → 11 → 23, and 23 is the first value past 20. diagrammatic-reasoning-s10-q08 The machine pairs arrivals: 3 is stored, 4 triggers the output 7; then 6 is stored and 2 triggers the output 8. diagrammatic-reasoning-s10-q09 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. diagrammatic-reasoning-s10-q10 ★ 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. Source: https://learn.novusstreamsolutions.com/cognitive-skills/diagrammatic-reasoning