Learn by Novus · Open practice pack v1

Diagrammatic reasoning: transformations, flows, and rule diagrams: open practice pack: learner worksheet

100 untimed questions across 10 authored sections.

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

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?

  1. 5
  2. 12
  3. 13
  4. 36

Answer:

2. diagrammatic-reasoning-s01-q02

A box labelled 'Double' receives the number 7. What is the output?

  1. 9
  2. 14
  3. 21
  4. 49

Answer:

3. diagrammatic-reasoning-s01-q03

A box labelled 'Reverse' receives the letter sequence P-Q-R. What sequence comes out?

  1. P-Q-R
  2. Q-P-R
  3. R-Q-P
  4. R-P-Q

Answer:

4. diagrammatic-reasoning-s01-q04

A box labelled 'Remove the last item' receives the list: apple, pear, plum. What list comes out?

  1. apple, pear
  2. pear, plum
  3. apple, plum
  4. apple, pear, plum

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?

  1. Up
  2. Down
  3. Left
  4. Right

Answer:

6. diagrammatic-reasoning-s01-q06

A box labelled 'Swap the first and last symbols' receives the sequence ★ ● ▲ ■. What comes out?

  1. ■ ● ▲ ★
  2. ● ★ ■ ▲
  3. ■ ▲ ● ★
  4. ★ ■ ▲ ●

Answer:

7. diagrammatic-reasoning-s01-q07

A box labelled 'Halve' receives the number 26. What is the output?

  1. 12
  2. 13
  3. 24
  4. 52

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?

  1. A white triangle
  2. A black square
  3. A white circle
  4. A black triangle

Answer:

9. diagrammatic-reasoning-s01-q09

A box labelled 'Repeat the whole sequence twice' receives the sequence A-B. What comes out?

  1. A-A-B-B
  2. A-B-A-B
  3. A-B-B-A
  4. B-A-B-A

Answer:

10. diagrammatic-reasoning-s01-q10

A box labelled 'Subtract 6' receives the number 6. What is the output?

  1. 0
  2. 1
  3. 6
  4. 12

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?

  1. 13
  2. 16
  3. 11
  4. 10

Answer:

12. diagrammatic-reasoning-s02-q02

The number 12 enters [Halve] and the result enters [Subtract 2]. What is the output?

  1. 4
  2. 5
  3. 8
  4. 10

Answer:

13. diagrammatic-reasoning-s02-q03

The letters C-A-T enter [Reverse] and the result enters [Remove the last letter]. What comes out?

  1. A-T
  2. C-A
  3. T-C
  4. T-A

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?

  1. North
  2. East
  3. West
  4. South

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?

  1. 8, 6, 4, 2
  2. 8, 6, 4
  3. 4, 6, 8
  4. 6, 4, 2

Answer:

16. diagrammatic-reasoning-s02-q06

The number 3 enters [Square] and the result enters [Add 1]. What is the output?

  1. 16
  2. 7
  3. 9
  4. 10

Answer:

17. diagrammatic-reasoning-s02-q07

A white circle enters [Toggle shading] and the result enters [Rotate 90° clockwise]. What comes out?

  1. A black circle
  2. A white circle
  3. A black square
  4. A white square

Answer:

18. diagrammatic-reasoning-s02-q08

The word STAR enters [Swap the first and last letters] and the result enters [Reverse]. What comes out?

  1. RATS
  2. RTAS
  3. SATR
  4. TARS

Answer:

19. diagrammatic-reasoning-s02-q09

The number 18 enters [Subtract 4] and the result enters [Halve]. What is the output?

  1. 9
  2. 5
  3. 7
  4. 14

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?

  1. 16
  2. 14
  3. 12
  4. 10

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?

  1. It adds 3
  2. It doubles
  3. It squares
  4. It adds 5

Answer:

22. diagrammatic-reasoning-s03-q02

A mystery box turns 10 into 7, 8 into 5, and 6 into 3. What is its rule?

  1. It halves
  2. It subtracts 2
  3. It subtracts 4
  4. It subtracts 3

Answer:

23. diagrammatic-reasoning-s03-q03

A mystery box turns CAT into TAC and STOP into POTS. What is its rule?

  1. It reverses all the letters
  2. It swaps only the first and last letters
  3. It moves the last letter to the front
  4. It writes the letters in alphabetical order

Answer:

24. diagrammatic-reasoning-s03-q04

A mystery box turns 4 into 16, 5 into 25, and 7 into 49. What is its rule?

  1. It multiplies by 4
  2. It adds 12
  3. It squares
  4. It multiplies by 5

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?

  1. It repeats the whole sequence
  2. It copies the first symbol onto the end
  3. It copies the last symbol onto the front
  4. It reverses the sequence

Answer:

26. diagrammatic-reasoning-s03-q06

A mystery box turns 7 into 15, 10 into 21, and 4 into 9. What is its rule?

  1. It doubles, then adds 1
  2. It adds 8
  3. It doubles, then subtracts 1
  4. It triples, then subtracts 6

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?

  1. It turns every figure black
  2. It turns every figure white
  3. It changes the shape but keeps the shading
  4. It swaps the shading but keeps the shape

Answer:

28. diagrammatic-reasoning-s03-q08

A mystery box turns 12 into 6, 20 into 10, and 8 into 4. What is its rule?

  1. It subtracts 6
  2. It subtracts 10
  3. It halves
  4. It divides by 3

Answer:

29. diagrammatic-reasoning-s03-q09

A mystery box turns BOLT into BOL, RAIN into RAI, and TREE into TRE. What is its rule?

  1. It removes the last letter
  2. It removes the first letter
  3. It keeps only the first letter
  4. It removes all vowels

Answer:

30. diagrammatic-reasoning-s03-q10

A mystery box turns 2 into 8. Which rule is consistent with BOTH 2→8 and 3→27?

  1. It multiplies by 4
  2. It cubes
  3. It adds 6
  4. It squares, then adds 4

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?

  1. 4 dots
  2. 6 dots
  3. 3 dots
  4. 5 dots

Answer:

32. diagrammatic-reasoning-s04-q02

A series of squares alternates: black, white, black, white. What colour is the next square?

  1. Black
  2. White
  3. Grey
  4. Striped

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?

  1. Up
  2. Right
  3. Left
  4. Down

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?

  1. 5 white dots
  2. 5 black dots
  3. 4 black dots
  4. 6 white dots

Answer:

35. diagrammatic-reasoning-s04-q05

A series of shapes shows: triangle, square, pentagon. Which shape comes next?

  1. Circle
  2. Triangle
  3. Octagon
  4. Hexagon

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?

  1. Top-left corner
  2. Bottom-left corner
  3. Top-right corner
  4. The centre

Answer:

37. diagrammatic-reasoning-s04-q07

What is the next number in the series: 2, 4, 3, 6, 5, 10, 9, ...?

  1. 18
  2. 11
  3. 8
  4. 13

Answer:

38. diagrammatic-reasoning-s04-q08

What is the next letter in the series: A, C, F, J, ...?

  1. N
  2. M
  3. O
  4. P

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?

  1. A large arrow pointing left
  2. A medium arrow pointing left
  3. A small arrow pointing up
  4. A small arrow pointing left

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?

  1. 4
  2. 6
  3. 5
  4. 7

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?

  1. 8
  2. 7
  3. 10
  4. 11

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?

  1. 6
  2. 24
  3. 12
  4. 5

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?

  1. 15
  2. 5
  3. 10
  4. 4

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?

  1. ORANG
  2. EGNARO
  3. ORANGE
  4. GNARO

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?

  1. 6
  2. 5
  3. 18
  4. 9

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?

  1. Depot A
  2. Depot B
  3. Depot C
  4. It cannot be determined

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?

  1. A 3 kg parcel, not fragile
  2. A 1 kg parcel, marked fragile
  3. A 2.5 kg parcel, marked fragile
  4. A 1.8 kg parcel, not fragile

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?

  1. 4
  2. 14
  3. 12
  4. 24

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?

  1. 9
  2. 13
  3. 36
  4. 23

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?

  1. 3
  2. 6
  3. 9
  4. 15

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?

  1. Green
  2. Red
  3. Amber
  4. Flashing amber

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?

  1. Locked
  2. Closed
  3. Open
  4. It cannot be determined

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?

  1. Idle
  2. Ready
  3. Refunding
  4. Printing

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?

  1. Idle
  2. Printing
  3. Ready
  4. The machine jams

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?

  1. Floor 3
  2. Floor 5
  3. Floor 4
  4. Floor 2

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?

  1. Spin
  2. Rinse
  3. Wash
  4. Done

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?

  1. Unlocked
  2. Locked
  3. Jammed
  4. It cannot be determined

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?

  1. Stations 1 and 2
  2. Station 2 only
  3. Stations 1, 2 and 3
  4. Stations 1 and 3

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?

  1. Fresh
  2. Tired
  3. Exhausted
  4. It cannot be determined

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?

  1. 0p
  2. 10p
  3. 20p
  4. 30p

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?

  1. 10
  2. 12
  3. 8
  4. 36

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?

  1. R-S-T
  2. S-R-T
  3. R-T-S
  4. T-S-R

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 → [◆] → [●]?

  1. 11
  2. 14
  3. 10
  4. 19

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?

  1. X-Y
  2. Z
  3. Y-Z
  4. X-Z

Answer:

65. diagrammatic-reasoning-s07-q05

A single mystery box turns 3 into 9 and 5 into 15. What is its rule?

  1. It squares
  2. It adds 6
  3. It multiplies by 3
  4. It adds 10

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?

  1. Add 3
  2. Double
  3. Subtract 5
  4. Add 5

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?

  1. A white arrow pointing right
  2. A black arrow pointing right
  3. A black arrow pointing up
  4. A black arrow pointing left

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?

  1. Halve first, then Add 2
  2. Add 2 first, then Halve
  3. Either order gives 5
  4. Neither order can give 5

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?

  1. It removes the first item
  2. It keeps only the first item
  3. It reverses again
  4. It removes the last item

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?

  1. 9
  2. 15
  3. 24
  4. 6

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?

  1. 12
  2. 20
  3. 48
  4. 24

Answer:

72. diagrammatic-reasoning-s08-q02

Start with 2. Keep doubling until the number exceeds 30. How many doublings are performed?

  1. 5
  2. 4
  3. 3
  4. 6

Answer:

73. diagrammatic-reasoning-s08-q03

Start with 100. Repeatedly subtract 15 until the result is 40 or less. What is the final number?

  1. 40
  2. 25
  3. 55
  4. 45

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?

  1. 3
  2. 5
  3. 4
  4. 6

Answer:

75. diagrammatic-reasoning-s08-q05

Start with the word DIAGRAMS. Remove the last letter repeatedly until exactly 4 letters remain. What is left?

  1. DIAG
  2. DIAGR
  3. RAMS
  4. DIA

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?

  1. 7
  2. 14
  3. 6
  4. 12

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?

  1. 9
  2. 6
  3. 7
  4. 8

Answer:

78. diagrammatic-reasoning-s08-q08

A loop halves the number while it is even. Start with 48. What is the final number?

  1. 6
  2. 3
  3. 1
  4. 24

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?

  1. 4
  2. 5
  3. 2
  4. 8

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?

  1. It stops at 10
  2. It stops at 11
  3. It stops after exactly five passes
  4. It never stops

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?

  1. The Add 5 box
  2. The Double box
  3. Both boxes
  4. Neither box

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?

  1. The Reverse box
  2. The Remove box
  3. Both boxes
  4. Neither box

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?

  1. The Triple box
  2. Both boxes
  3. The Subtract 2 box
  4. Neither box

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?

  1. The Rotate box
  2. Both boxes
  3. Neither box
  4. The Toggle shading box

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?

  1. The Add 1 box
  2. The Double box
  3. The Subtract 3 box
  4. It cannot be determined

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?

  1. The first Double box
  2. The second Double box
  3. The Subtract 4 box
  4. None of the boxes

Answer:

87. diagrammatic-reasoning-s09-q07

A box labelled 'Add 10' receives 7 and outputs 27. Which fault mode best describes its behaviour?

  1. It did nothing
  2. It applied its rule twice
  3. It subtracted instead of adding
  4. It worked correctly

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?

  1. The Subtract 8 box
  2. Both boxes
  3. Neither box
  4. The Halve box

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?

  1. The Reverse box
  2. The second Remove box
  3. None of the boxes
  4. The first Remove box

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?

  1. It doubled correctly in the first test but passed the input unchanged in the second
  2. It always works correctly
  3. It never works correctly
  4. It halves even numbers

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?

  1. A white arrow pointing south
  2. A black arrow pointing north
  3. A black arrow pointing south
  4. A black arrow pointing west

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?

  1. 19
  2. 16
  3. 13
  4. 22

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?

  1. 19
  2. 11
  3. 60
  4. 7

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?

  1. 64
  2. 8
  3. 16
  4. 32

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?

  1. A black arrow pointing down
  2. A white arrow pointing up
  3. A black arrow pointing right
  4. A black arrow pointing up

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?

  1. 23
  2. 21
  3. 19
  4. 20

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?

  1. 23
  2. 11
  3. 22
  4. 21

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?

  1. 7
  2. 8
  3. 6
  4. 9

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?

  1. 7
  2. 6
  3. 5
  4. 9

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?

  1. 12
  2. 9
  3. 18
  4. 6

Answer: