Analytical Reasoning & Intelligence Tests — Chapter 4

Direction Sense

Why this chapter matters: Direction sense is the most diagram-dependent family in Subject 12, and the most forgiving once the habit is fixed: every item is a walk, a turn, or a relative position, and every one of them is solved by drawing the path or the grid — never by holding it in your head. The script count behind this chapter (Section 10) finds 20 genuine direction-sense stems across 17 distinct source files, from an FPSC 2001 paper through PPSC 2019–2020 papers to a CSS MPT 2026 mock. Twenty stems is a small bank, and this chapter is honest about that: it teaches the five path/position types those stems actually use, works every genuine stem, and flags the one stem the banks themselves key two different ways (Section 6) rather than pretending the banks agree. If you can draw these twenty, you can do any direction item the papers set, because no new type appears outside them.

Status of this chapter (read first): this is AR-04, written 31 October 2026 in taxonomy order after AR-03. The Subject 12 structure page claimed no mark for this family at structure level because its paper-level spread had not been verified file by file; that verification is done in this run (Section 10), and the marks in the Exam Trend box below rest on it — not on the structure page’s counts alone. One correction to the structure page is recorded here, not hidden: its “22 unique stems, 18 files” figure includes two train-crossing stems whose topics merely contain the word “direction” (see Section 10). The genuine direction-sense bank is 20 stems across 17 files.

Exam Trend box

• 🔁 Most Repeated: Direction sense as a family — 20 genuine stems across 17 distinct source files, clearing the 🔁 paper-count limb (≥5 different papers) by a wide margin. The exam-paper sources alone are sixteen: FPSC papers of 2001, 2004, 2005, 2007, 2008, 2009, 2010 and 2015, and PPSC papers of 2019 and 2020 — plus one CSS MPT 2026 mock file.
• ⭐ Must Know: none claimed. The family is 🔁, but its 2024–2026 signal is a single 2026 mock-test stem (the trivial “opposite of East” item, Section 2.1), not a 2024–2026 exam paper. Direction sense is therefore taught as a high-frequency, always-available family, not as a must-know 2024–2026 item — the distinction matters, and this chapter does not blur it.
• 🆕 Newly Appeared / Recent Trend: none claimed. Direction items run continuously from FPSC 2001 to PPSC 2020; nothing in the bank is a first appearance of 2025–26.

1. The method — four steps, in order

1. Draw the compass before you read the stem. North up, South down, East right, West left. Every direction item in this bank is won or lost on whether the diagram exists.
2. Turns are relative to the facing direction, not to the map. Facing North, a right turn faces East; facing South, a right turn faces West; facing East, a right turn faces South; facing West, a right turn faces North. Left turns are the mirror of this. If you turn “right” on the map instead of on the walker, the item is already lost.
3. Track two things separately: where he ends, and which way he faces. A stem can ask either one, and the banks deliberately mix them (see the Cabinet 2004 trap in Section 6). Position is a north–south total and an east–west total; facing is the last turn’s result.
4. For distance from the start, cancel first, then use Pythagoras. Opposite legs cancel (12 km North and 18 km South leave 6 km South; 15 km East and 15 km West leave nothing). What is left is a right triangle: the bank’s triangles are 3–4–5 triangles (Section 3), so check that first before reaching for a square root.

2. Core notes — the five types the banks actually use

2.1 Compass basics and opposites

• Rule: the four cardinals in clockwise order are North → East → South → West → North. The opposite of any direction is two steps away: North ↔ South, East ↔ West.
• Worked example (banked): “The opposite of East is:” — West (CSS MPT 2026 full mock test). Trivial on its own, but it is the fact every other type in this chapter assumes.
• Facing and turning (the turn sequence). Work through the turns one at a time, updating the facing direction each time.
• Worked example (banked): “If you are standing with your face towards East, then you turn right, then again right, and then left. Which direction are you facing at the end?” — East → (right) South → (right) West → (left) South = South (PPSC Assistant Planning 2019; the same stem with the same answer, South, appears in PPSC Assistant BS-16 Planning & Development 2019). Two right turns reverse you; the final left turn steps you back one quarter-turn — it does not restore the start.

2.2 Walk-and-turn paths — direction from the start

• Rule: walk the path leg by leg on the diagram, then read the end point’s position against the start point. If the stem asks “in which direction is he from the starting place”, the answer is the quadrant (or cardinal) of the net displacement, not the last leg’s direction.
• Worked example (banked): “A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?” — South 5, then (facing South, right is West) West 3, then (facing West, left is South) South 5. Net: 10 km South, 3 km West = South-West (FPSC Inspector Customs / Preventive Officer 2015).
• Worked example (banked): “A man walks 3 km to his East then turns left and walks 3 km towards North then turns left and walks 3 km towards West. Indicate the correct direction in which he is in relation to his starting point” — East 3, then (facing East, left is North) North 3, then (facing North, left is West) West 3. Net: 3 km North, 0 east–west = North (PPSC Ziladar, Irrigation Department, 2020, in two bank files with the same answer).
• Worked example (banked, the direction-going trap): “If you start from point A and walk 5 kms towards the West, then turn right and walk 4 kms towards the North, then turn right again and walk 3 kms then which choice mentions the direction in which you are going” — facing West, right is North; facing North, right is East. The direction you are going on the last leg is East (FPSC Assistant Director, Cabinet Division, 2004). Note the trap: your position at the end is 2 km West and 4 km North of the start (North-West), but the stem does not ask your position — it asks the direction you are going. Answer the question that was asked (Section 6).

2.3 Walk-and-turn paths — distance from the start

• Rule: cancel opposite legs first (Section 1, step 4), then apply Pythagoras to what is left: distance² = (north–south net)² + (east–west net)². Check for a 3–4–5 triangle before computing anything else — all three distance stems in this bank are 3–4–5 triangles or straight-line cancellations.
• Worked example (banked, straight cancellation): “A person travels 12 km due North, then 15 km due East, after that 15 km due West and then 18 km due to south. How far is he from the starting point” — East 15 and West 15 cancel to nothing; North 12 and South 18 leave 6 km South = 6 km (FPSC Deputy Director FIA 2008). (The bank’s options print “60 km” twice — a printing slip in the options, not in the answer; the distance is 6 km.)
• Worked example (banked, 3–4–5): “A woman travels one mile due East, then 5 miles due South, then 2 miles due East and finally 9 miles due North. How far is she from her starting point?” — East total 3, South 5 and North 9 leave North 4. 3² + 4² = 25, so √25 = 5 miles (FPSC Assistant Director, Ministry of Overseas / Human Resources, 2005).
• Worked example (banked, 3–4–5): “A person starts walking towards north from a point and walks 3 km; then moves left and walks 2 km; again moves to his right and walks 1 km and finally moves to his right and walks 5 km. At what distance is he now from the starting point?” — North 3, then (left) West 2, then (right) North 1, then (right) East 5. Net: North 4, East 3. 3² + 4² = 25, so 5 km (FPSC Junior Admin Officer, Ministry of Defence, 2009).

2.4 Relative direction of two persons or places

• Rule: put the middle person or place at the origin, plot each other person on the grid, then read one person’s position against the other — not against the origin. The most common error is answering against the wrong reference point.
• Worked example (banked): “If x is west of y and y is north of z, towards which directions of x is z?” — put y at the origin: x is West of y, z is South of y. Against x, z is one step East and one step South = South-East (FPSC Assistant Director FIA 2001).
• Worked example (banked): “Point x is in North of point y and point y is East of point z. To which direction is point x with respect to z.” — z at the origin, y East of z, x North of y. Against z, x is East and North = North-East (FPSC Inspector ANF 2010).
• Worked example (banked): “If Amir is in the North of Bilal and Saad is in the West of Bilal. In which direction is Amir with respect to Saad?” — Bilal at the origin, Amir North, Saad West. Against Saad, Amir is East and North = North-East (PPSC Inspector 2020, Anti-Corruption Establishment, Punjab).
• Worked example (banked): “If A is to the south of B and C is to the east of B. In which direction is A with respect to C?” — B at the origin, A South, C East. Against C, A is West and South = South-West (PPSC Assistant, Labour Department, 2020).

2.5 Two walkers, and the clock-direction item

• Two walkers (separation). Plot both walkers from the same start, then measure between their end points — not from the start.
• Worked example (banked): “Zohaib and Ali depart from point X. Zohaib goes North and covers 3 km then turns right and covers 4 km. Ali goes West and covers 5 km, then turns right and covers 3 km. How far is Zohaib from Ali?” — Zohaib: North 3, then (right) East 4 → (East 4, North 3). Ali: West 5, then (right, facing West) North 3 → (West 5, North 3). Same northing, east–west gap 4 + 5 = 9 km (PPSC Ziladar, Irrigation Department, 2020).
• Clock direction (a rotated dial). A clock face is a compass in disguise: 12, 3, 6 and 9 on the dial are four directions 90° apart. If the stem fixes one hand to a compass direction, rotate the whole dial by that amount and read the other hand off the rotated dial.
• Worked example (banked): “Azam Ali put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In which direction the minute hand will point at 9.15 P.M.?” — at 6 P.M. the hour hand sits on the 6 of the dial, and that 6-direction is North, so the dial is rotated 180° from normal (the 12-direction is South, the 3-direction is West, the 9-direction is East). At 9:15 the minute hand sits on the 3 of the dial, and the 3-direction on this rotated dial is West (FPSC Inspector Customs / Preventive Officer 2015).

3. Master table — type → method → bank example

4. Rapid-fire one-liners

• Compass first, stem second: draw North–East–South–West before reading a single leg.
• Turns belong to the walker, not the map: facing South, right is West.
• Position and facing are different questions — answer the one the stem asked (Cabinet 2004: going East, position North-West).
• Cancel opposites before Pythagoras: 15 East and 15 West are already gone.
• 3–4–5 first: if the net legs are 3 and 4, the distance is 5 — do not compute a square root you do not need.
• Relative direction: put the middle point at the origin, then read against the asked reference, not the origin.
• Two walkers: measure end point to end point, never from the start.
• Clock items: rotate the whole dial by the given hand, then read the asked hand.
• Upside down, in these papers, is a vertical flip only — face stays South, left stays East (Section 6) — but know that one bank printing keys it West.

5. Most-asked facts

• 🔁 Walk-and-turn paths are the family’s core: 7 of the 20 genuine stems are path items (direction from start, direction going, or distance from start), across FPSC 2004, 2005, 2008, 2009, 2015 and PPSC 2020. If a reasoning section sets one direction item, it is most likely a path item.
• 🔁 Relative-direction items are the second core: 4 of the 20 genuine stems, across FPSC 2001, FPSC 2010, PPSC 2020 (×2). They are all solved by the same origin trick (Section 2.4) — learn the trick once, not the four answers.
• The 3–4–5 triangle is the family’s only distance pattern: both Pythagoras stems in the bank resolve to 5 (5 miles, 5 km). A direction distance that is not a cancellation is, in this bank, a 3–4–5 triangle.
• Turn sequences and the clock item are one-offs each in this bank, but they are the items that separate full marks from partial marks — they are solved by method (Section 1), not by memorising more paths.

6. Traps & confusions

• Direction going vs direction from start (the Cabinet 2004 trap). 5 West, right North 4, right East 3: the direction you are going is East, but your position is North-West of the start. The stem asks one of these two words — circle it before you compute.
• Right and left after a turn (the facing trap). “Turns to the right” after walking South means West, not East. Every path error in this bank is a turn read off the map instead of off the walker (Section 1, step 2).
• The upside-down stem — bank keys split, read this before you answer it. Four bank files carry the same stem, “a man standing upside down with his face towards South, where will his left hand point?”: FPSC Inspector ANF 2010, PPSC Sub-Inspector (Service Quota) 2019 and PPSC Punjab Police Sub-Inspector 2019 all key it East; FPSC Public Relations Officer 2007 keys it West. The three East keys follow the papers’ convention, and this chapter teaches that convention: “upside down” here is treated as a vertical flip only — the face stays South and the left hand stays East (the hand that was East before the flip is still East after it). Do not overthink it as a three-dimensional handstand, which is what produces West: the papers do not use that model, and the majority key is East. The split is recorded here so a student who meets the 2007 printing is not confused by it — but the answer to learn is East.
• “Encoding” and trains are not direction sense. The topic rule that counts this chapter also catches two train-crossing stems (“crossing a man walking in the same direction”, “crossing in opposite direction”) because their topics contain the word “direction” — but they are MA-03 train problems (speeds and times), not direction sense, and they are excluded from this chapter’s teaching and from the 20 genuine stems (Section 10). Train “opposite direction” belongs to MA-03, not here.
• No diagonal-walk or angle items in this bank. Standard reasoning books also teach 45° turns (North-East facing changes) and shadow-direction items (morning/evening sun), but no bank stem in scope uses them. They are not taught here, and they are not smuggled in as worked examples from outside the banks.

7. Memory tricks

• “NESW, clockwise”: North, East, South, West round the compass in clockwise order. Opposites are two steps apart; a right turn is one step clockwise, a left turn one step counter-clockwise.
• “Walker, not map”: say whose right it is before every turn — the walker’s right, never the map’s right.
• “Cancel, then 3–4–5”: the two words for every distance item. Cancel first; if 3 and 4 remain, the answer is 5.
• “Middle at the origin”: for every relative-direction item, put the shared middle person at (0, 0) and plot the other two — the answer reads itself off the grid.
• “East, right, right, left → South”: the PPSC turn-sequence stem as the anchor example — two rights reverse you, the final left steps you back one quarter-turn.

8. Visuals (specs only — site build renders these)

• Compass rose: the four cardinals plus the four intercardinals (NE, SE, SW, NW), placed before Section 2, with the clockwise order marked.
• Path diagrams: each Section 2.2/Section 2.3 example as a labelled walk (legs in order, net displacement as a dashed line, 3–4–5 triangle highlighted where it applies).
• Relative-direction grids: each Section 2.4 example as a 3 × 3 grid with the middle point at the origin.
• Clock-dial diagram: the Section 2.5 timepiece item with the dial rotated 180° (6→North, 3→West) and the 9:15 minute hand marked.
• Turn-sequence strip: the East → South → West → South sequence as four compass arrows in a row.

9. Practice this topic

Pull a timed set from the verified banks using the practice query in the front-matter (topic tags Direction Sense / Directions / Distance direction): 20 genuine stems across 17 distinct files. Book mode: ← Previous: Coding-Decoding (AR-03) · Next: Blood Relations (AR-05) →

Sources & count (Section 10 honesty note). Count by script hidden_files/goldmine-notes-count-ar04.py (counts JSON hidden_files/goldmine-notes-ar04-counts.json), same bank dirs and topic-based classification order as the Subject 12 structure count (hidden_files/goldmine-notes-count-ar12.py): 584 files / 56,434 questions scanned; 23 rows including duplicates; 22 unique script stems across 18 distinct files; filename-year files 2026: 1. Of those 22, 20 are genuine direction-sense stems across 17 distinct files and 2 are false positives: the two subject-arithmetic-problems-on-trains.json stems (“crossing a man walking in the same direction” and “crossing in opposite direction”) — their topics contain the word “direction” but their content is train speed/time (MA-03), and the structure page’s “train topics excluded” rule fails on them because the word “train” sits in the file name, not the topic. They are excluded from teaching, from the 20, and from the practice query, and the structure page’s “22 unique, 18 files” figure is corrected to 20 / 17 here. Genuine-stem sources: FPSC Assistant Director Cabinet Division 2004 (1), FPSC Assistant Director FIA 2001 (1), FPSC Assistant Director Ministry of Overseas / Human Resources 2005 (1), FPSC Deputy Director FIA 2008 (1), FPSC Inspector ANF 2010 (2), FPSC Inspector Customs / Preventive Officer 2015 (2), FPSC Junior Admin Officer Ministry of Defence 2009 (1), FPSC Public Relations Officer 2007 (1), PPSC Sub-Inspector Service Quota 2019 (1), PPSC Assistant BS-16 Planning & Development 2019 (1), PPSC Inspector 2020 Anti-Corruption Establishment (1), PPSC Ziladar Research / Irrigation 2020 (1), PPSC Assistant Labour Department 2020 (1), PPSC Assistant Planning 2019 (1), PPSC Punjab Police Sub-Inspector 2019 Service Quota (1), PPSC Ziladar Irrigation Department paper 2, 2020 (2), CSS MPT 2026 full mock test (1) — 20 stems, 17 files (the two Ziladar 2020 files and the two upside-down PPSC files are counted by file, and the four upside-down wordings are four script rows of one stem family). Classification is topic-based only, so untagged direction items inside general papers are not counted: 20 is a floor, stated honestly, not an estimate. Every banked answer taught here was verified by hand against its stem in this run: the 3–4–5 distances (5 miles, 5 km), the 6 km cancellation, the 9 km two-walker gap, the Cabinet direction-going East, the clock West, and all four relative-direction quadrants were recomputed leg by leg. The upside-down stem is the one stem not settled by recomputation alone: its four bank keys split 3 East to 1 West (Section 6), and this chapter teaches the majority East convention with the split flagged, not hidden. No fact in this chapter comes from memory; methods are standard procedural types, and every worked example is a bank stem with its banked answer.