map-route-reasoning-s01-q01
Clockwise follows the compass in the order north → east → south → west, so one quarter turn from north points you east.
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.
Clockwise follows the compass in the order north → east → south → west, so one quarter turn from north points you east.
A 180° turn always points you in the exact opposite direction, and the opposite of east is west.
Anticlockwise runs against the compass order: south → east → north → west. One quarter turn anticlockwise from south is east.
The sun rises in the east, so you begin facing east; when you face east, a left turn points you north.
Unless a map states otherwise, the convention is north at the top, which also puts east on the right and west on the left.
Track each quarter turn: west → north (90°) → east (180°) → south (270°). Alternatively, 270° clockwise equals 90° anticlockwise.
Place the three on a north–south line: café, then fountain, then library. The library sits at the northern end.
Two 90° turns in the same direction make 180°, which always leaves you facing the opposite way, south instead of north.
Right and left depend on which way you face: when travelling south, your right-hand side points west.
Directions reverse when you swap viewpoints: if the village is west of the bridge, the bridge must be east of the village.
Reversing a route swaps every turn: because you approach each corner from the opposite side, left turns become right turns and vice versa.
Two people facing each other have mirrored sides: whatever is on your right is on the other person's left.
Update your heading one turn at a time: north → east (right) → south (right) → east (left). Tracking step by step avoids losing count.
Follow each turn: east → north (left) → west (left) → north (right). A quick check is to net the turns: two lefts and a right equal one left overall.
When a map is turned to match your facing direction, the map's left edge lines up with your own left side, and facing south, your left hand points east.
Turning around to retrace your steps flips your left and right, so anything that was on your right on the way in is on your left on the way out.
A right and a left cancel each other, leaving one net right turn: 90° clockwise from west is north.
Three quarter turns clockwise total 270°, which is the same as one quarter turn anticlockwise: north → west.
The northbound walker's right is the east side of the street. Facing south, east falls on your left, so the southbound walker sees the shop on their left.
Work each person separately: your right turn takes north to east, while your friend's right turn takes south to west. East and west are opposites, so you still face away from each other.
Compare the coordinates: only x changes, rising from 2 to 5. An increasing x-value on this grid means movement east.
The x-values match, so the points sit on the same north–south line; subtract the y-values: 6 − 1 = 5 units.
Moving north keeps the column letter the same and increases the row number by one, taking C2 to C3.
With no diagonal moves, add the east–west and north–south differences separately: (4 − 1) + (5 − 1) = 3 + 4 = 7 blocks.
Furthest west means the smallest x-value; ignore the y-values entirely. The x-values are −3, 1, 4, and 0, and −3 is the smallest.
Average each coordinate: (2 + 8) ÷ 2 = 5 for x, and y stays at 4, giving a midpoint of (5, 4).
Judge each axis separately: D is east of B, and row 4 is north of row 2. East plus north combines into north-east.
Net each axis: east 6 then west 2 leaves x = 4, and the single northward leg leaves y = 2, so the drone ends at (4, 2).
The points are 4 grid squares apart along the same line; multiply by the scale: 4 × 500 m = 2,000 m, which is 2 km.
Corner-only (diagonal) neighbours differ by one step in both the column and the row. B2 shifts one column west and one row south of C3, while the others share a full edge.
Equal legs in opposite directions cancel out completely: you walked 10 km in total but finished exactly where you began.
Opposite directions subtract rather than add: 6 km north minus 2 km south leaves a net 4 km north of the start.
The two legs form the sides of a right angle, so use Pythagoras: √(3² + 4²) = √25 = 5 km, the classic 3-4-5 triangle.
Handle each axis separately: the 2 km west and 2 km east cancel, leaving only the 5 km northward leg.
Distance travelled and final displacement are different things: a full lap covers 400 m of ground but ends zero metres from the start.
Total the eastward and westward movement separately: 8 km east against 3 + 2 = 5 km west leaves a net 3 km east.
Equal southward and westward legs place you diagonally from the start, exactly halfway between south and west: south-west.
The legs meet at a right angle, so apply Pythagoras: √(5² + 12²) = √169 = 13 km, the 5-12-13 triangle.
Add the legs with direction in mind: 7 km north against 4 + 3 = 7 km south nets to zero, so the walker is back where they began.
Net each axis: east 2 and west 2 cancel, while north 1 against south 3 leaves 2 km south. Splitting a route into axes makes multi-leg journeys manageable.
Both buildings lie in the same direction from the station, so compare the counts directly: one street away is closer than two.
Chain the relationships: two eastward steps in a row keep everything on the same line, so the market must lie east of the fountain.
Fix the known end first: park at the west, school in the middle, which forces the pool to the eastern end.
Both clues share the stadium, which pins the order down as cinema, then stadium, then hospital, putting the stadium second.
To reverse a route, undo the legs in reverse order with opposite directions: the final eastward block becomes westward first, then the northward block becomes southward.
Both villages lie the same way from the signpost, so subtract the distances: 5 − 3 = 2 km separates them.
When destinations lie in opposite directions from the same point, add the distances: 3 + 5 = 8 km, passing the signpost on the way.
Reversing a route reverses the order of landmarks, but the middle item of three stays in the middle either way.
Facing the café means facing north, and when you face north, west lies on your left-hand side.
Chain the two clues into one route: two blocks east plus one block north makes three blocks of walking in total.
Add the journey time to the departure: 09:20 plus 25 minutes is 09:45, with no hour boundary to cross.
List the departures from the first one: 07:00, 07:15, 07:30. The first train after 07:20 leaves at 07:30, a 10-minute wait.
Compare durations, not arrival times: Bus A takes 45 minutes while Bus B takes 35 minutes, so the later departure is actually the quicker ride.
Cross the hour in two steps: 15 minutes takes you to 11:00, and the remaining 15 minutes lands on 11:15.
Work backwards from the deadline: 17:00 minus 45 minutes is 16:15, the last moment a full-length visit still fits.
Bridge the hour: 14:32 to 15:00 is 28 minutes, then 15:00 to 15:18 adds 18 more, giving 46 minutes in total.
The buses run at :00 and :30 past each hour, so after a 12:10 arrival the next one leaves at 12:30. A 20-minute wait.
Work backwards from the deadline: to arrive by 09:00 you must leave by 08:20, and the latest departure at or before that is 08:15, arriving 08:55.
Split the journey at midnight: 23:40 to 00:00 is 20 minutes, and 00:00 to 06:10 is 6 hours 10 minutes, totalling 6 hours 30 minutes.
Step through the timetable: 06:00, 06:40, 07:20, 08:00, 08:40. The first departure strictly after 08:30 is 08:40.
A shorter distance is irrelevant if the route cannot be completed: the closed bridge removes Route 2 from consideration entirely.
Recalculate before comparing: the detour makes Route C 11 + 5 = 16 km, so Route A's 12 km is now the shortest of the three.
Convert each route to time using time = distance ÷ speed: Route A takes 20 minutes while Route B takes 30, so the longer road is the faster journey.
Subtract the two journey times: 45 − 30 = 15 minutes saved, which is the trade-off you weigh against the £2 cost.
Compare the permitted route with the direct one: 5 − 3 = 2 additional blocks caused by the one-way restriction.
Three sites give six orders in total, and the before-constraint holds in exactly half of them: P-Q-R, Q-P-R, and Q-R-P.
Check each distance against the 150 km range: only Route C, at 160 km with nowhere to refuel, exceeds what the tank can cover.
Total the legs first, 10 + 25 + 5 = 40 minutes, then subtract from the deadline: 09:00 minus 40 minutes is 08:20.
Test each constraint against the vehicle: the lorry is too tall for Route A and too heavy for Route C, so the longer Route B is the only lawful option.
Apply each closure rule to the day in question: Monday rules out North Road, the resurfacing rules out East Lane, but South Road only closes at weekends, so it is open.
The intercardinal directions combine the names of their neighbours: halfway between north and east is north-east.
Rotate 90° clockwise from north and you face east; each cardinal direction sits 90° further round (south 180°, west 270°).
South is 180° and west is 270°; a bearing of 225° falls exactly halfway between them, which is south-west.
Quarter turns work on diagonal headings too: 90° clockwise from north-east (045°) is 135°, which is south-east.
A return bearing is the outward bearing plus or minus 180°: 060° + 180° = 240° points exactly the opposite way.
North-east and south-west are exact opposites, so equal distances along them cancel completely, just as north and south would.
Reversing a bearing adds 180° (subtract instead if that would pass 360°): 045° + 180° = 225°.
Translate the bearings first: 180° is south and 270° is west. Equal legs south then west leave the ship south-west of where it began.
East is 090° and south is 180°, so 135° sits exactly halfway between them: south-east.
The legs are 4 km east then 4 km north, so the finish lies equally east and north of the start: a diagonal of north-east, which is bearing 045°.
Include the wait as part of the journey: 40 + 10 + 25 = 75 minutes, which is 1 hour 15 minutes door to door.
Add the hour first, then the minutes: 09:10 plus 1 hour is 10:10, plus 15 minutes gives 10:25.
Average speed is total distance over total time: 100 km in 2 hours gives 50 km/h. Because both legs took equal time, the simple average happens to agree.
Convert to the same unit before adding: 800 m is 0.8 km, and 1.5 + 0.8 = 2.3 km.
You miss the 11:00 sailing by five minutes, so the next departure is 45 minutes later at 11:45. A 40-minute wait from 11:05.
Because all three stops lie on the way to the furthest one, travel out to the pool and back, calling at the others en route: 6 km out plus 6 km back is 12 km.
Total each type separately, then combine: 3 × 20 = 60 minutes travelling and 2 × 12 = 24 minutes waiting makes 84 minutes, or 1 hour 24 minutes.
Add the legs, 35 + 10 = 45 minutes, then count back from the deadline: 18:00 minus 45 minutes is 17:15.
Build the full time for each option before comparing: the coach totals 80 + 10 = 90 minutes against the train's 50, a difference of 40 minutes.
Average speed uses the full elapsed time, rest included: 20 km in 90 minutes (1.5 hours) gives 20 ÷ 1.5 ≈ 13.3 km/h.
Every shortest route is an arrangement of the letters E, E, E, N, N; count the arrangements: 5! ÷ (3! × 2!) = 10.
Count the routes through the closed point and subtract: 2 ways from (0, 0) to (1, 1) times 2 ways onward makes 4 blocked routes, leaving 6 − 4 = 2.
Trace it step by step: south → east (left 90°) → west (right 180°) → south (left 90°). The left and right turns net to zero, returning you to your original heading.
Build the line clue by clue: M, then Q (between M and N), then N, then P, then R. Reading west to east gives M-Q-N-P-R, with N third of five.
Add the journey time to each departure: the 10:40 arrives at 11:35, within the deadline, but the 11:20 arrives at 12:15, which is too late.
The legs run 10 km east then 10 km south, placing the ship equally east and south of the start: that diagonal is south-east, bearing 135°.
Test each option against the time: the bridge shut at 20:00, the next ferry is not until 21:30, but the tunnel never closes, so it is the only immediate crossing.
The detour replaces one closed block with three (north, east, south), so the journey becomes 2 direct blocks plus the 3-block detour: 5 in total.
Together they close the 18 km gap at 4 + 5 = 9 km/h, so they meet after 2 hours; in that time Ali has walked 4 × 2 = 8 km from the west end.
Going straight to the bank means arriving at 14:10 and finishing by 14:20, before it closes. Visiting anywhere else first delays the bank arrival to 14:30 at the earliest, after closing, so the bank has to come first.