About Direction Sense Test
Direction questions describe a route made of straight stages and then ask where the person ends up. Every stage is a vector, so the reliable method is to track the north-south distance and the east-west distance separately and combine them at the end. Trying to picture the whole route in your head is where mistakes come from.
What you need to understand
- Write the north-south movement as one running total and the east-west movement as another.
- Movement in opposite directions cancels. North and south subtract, as do east and west.
- The two running totals are perpendicular, so together they form a right angled triangle.
- The distance from the start is the hypotenuse of that triangle, found with Pythagoras.
- The direction from the start is decided by the signs of the two totals, not by the order of the stages.
How to work through these questions
- Read the whole route, then write the stages down in order.
- Add every northward stage and subtract every southward one to get the net north-south distance.
- Do the same with east and west to get the net east-west distance.
- For a distance, square both totals, add them and take the square root.
- For a direction, use the signs: positive north with positive east is north-east, and so on.
Mistakes that cost marks
- Adding the lengths of the stages instead of combining directions.
- Using the longest single stage rather than the net movement in each direction.
- Forgetting that a stage in the opposite direction reduces the total rather than adding to it.
- Taking the square root of the sum of the two totals rather than the sum of their squares.
- Assuming the final direction follows the last stage, when it depends on the net movement.
Worked example
A person walks 6 metres north, then 8 metres east, then 3 metres south, then 3 metres north. How far is the person from the starting point?
- The northward movement is 6 plus 3, which is 9 metres north.
- The southward movement is 3 metres, so the net north-south distance is 9 minus 3, which is 6 metres north.
- The eastward movement is 8 metres and there is no westward movement, so the net east-west distance is 8 metres east.
- The two totals form a right angled triangle with legs 6 and 8. Since 6 squared is 36 and 8 squared is 64, the square of the hypotenuse is 100.
- The square root of 100 is 10, so the person is 10 metres from the start.
Answer: 10 metres
Practice questions with answers
A few Direction Sense Test questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
A person walks along the following route, turning after each stage.
6 metres to the west; 15 metres to the south; 15 metres to the north; 15 metres to the north; 8 metres to the east; 6 metres to the east
How far is the person from the starting point?
Answer: Option B — with explanation
The southward and northward stages cancel, as do the westward and eastward ones, so only the first two stages move the person.
That leaves a right angled triangle with legs 15 metres and 8 metres.
15 squared is 225, 8 squared is 64, and 225 + 64 = 289.
The square root of 289 is 17 metres.
Common mistakes
- subtracted the legs instead of using a right angled triangle: 7
- added the two legs instead of using a right angled triangle: 23
- an arithmetic slip in the final step: 18
Question 2
A person walks along the following route, turning after each stage.
19 metres to the east; 8 metres to the west; 1 metres to the south; 29 metres to the north
In which direction is the person from the starting point?
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A
North-West
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B
North-East
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C
South-East
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D
South-West
Answer: Option B — with explanation
Northward and southward movement cancels down to 29 minus 1, which is 28 metres north.
Eastward and westward movement cancels down to 19 minus 8, which is 11 metres east.
The person is therefore north and east of the start, that is, to the north-east.
Common mistakes
- reversed both pairs of stages: South-West
- mixed up the northward and southward stages: South-East
- mixed up the eastward and westward stages: North-West
Question 3
A person walks along the following route, turning after each stage.
13 metres to the west; 24 metres to the east; 7 metres to the north; 11 metres to the south; 13 metres to the east; 11 metres to the north
How far is the person from the starting point?
Answer: Option A — with explanation
The southward and northward stages cancel, as do the westward and eastward ones, so only the first two stages move the person.
That leaves a right angled triangle with legs 7 metres and 24 metres.
7 squared is 49, 24 squared is 576, and 49 + 576 = 625.
The square root of 625 is 25 metres.
Common mistakes
- added the two legs instead of using a right angled triangle: 31
- subtracted the legs instead of using a right angled triangle: 17
- an arithmetic slip in the final step: 26
Question 4
A person walks along the following route, turning after each stage.
12 metres to the south; 17 metres to the north; 17 metres to the east; 14 metres to the west
In which direction is the person from the starting point?
-
A
North-East
-
B
South-West
-
C
North-West
-
D
South-East
Answer: Option A — with explanation
Northward and southward movement cancels down to 17 minus 12, which is 5 metres north.
Eastward and westward movement cancels down to 17 minus 14, which is 3 metres east.
The person is therefore north and east of the start, that is, to the north-east.
Common mistakes
- mixed up the eastward and westward stages: North-West
- reversed both pairs of stages: South-West
- mixed up the northward and southward stages: South-East
Question 5
A person walks along the following route, turning after each stage.
15 metres to the east; 7 metres to the east; 15 metres to the west; 24 metres to the north; 10 metres to the north; 10 metres to the south
How far is the person from the starting point?
Answer: Option A — with explanation
The southward and northward stages cancel, as do the westward and eastward ones, so only the first two stages move the person.
That leaves a right angled triangle with legs 24 metres and 7 metres.
24 squared is 576, 7 squared is 49, and 576 + 49 = 625.
The square root of 625 is 25 metres.
Common mistakes
- an arithmetic slip in the final step: 26
- added the two legs instead of using a right angled triangle: 31
- subtracted the legs instead of using a right angled triangle: 17
Frequently asked questions
How do I solve a direction sense question?
Track two running totals, one for north-south and one for east-west. At the end of the route the two totals give you both the distance and the direction.
Why do I add and subtract the stages?
Because movement in opposite directions cancels. A stage north and an equal stage south leave you where you were, so the totals rather than the stage lengths are what matter.
When do I use Pythagoras?
When the net movement has both a north-south part and an east-west part. Those two parts are perpendicular, so they form the legs of a right angled triangle and the distance from the start is the hypotenuse.
How do I decide the final direction?
From the signs of the two totals. North and east together give north-east, south and east give south-east, and so on. If one total is zero the direction is simply the other one.
Does the order of the stages matter?
Not for the answer. The net movement is the same whatever order the stages are walked in, which is exactly why adding up the totals works.
