Direction Sense Test Questions and Answers

Answer: A

The order is Right, Right, Right.

Facing south, a right turn faces west, a second right turn faces north, and a third right turn faces east. Three right turns are the same as one left turn, and a left turn from south faces east.

The other orders end elsewhere. Left, Left, Left: east, north, west. Left, Right, Right: east, south, west. Right, Left, Right: west, south, west. Only the first sequence finishes facing east.

Answer: A

Sanjay is coming from the North.

In the morning the Sun is in the east, so shadows fall towards the west. Sanjay's shadow falls to his right, so his right hand points west. A person whose right is west is facing south.

Walking while facing south, Sanjay is coming from the north. Shivani walking east does not affect the answer; it only tells us she meets him. If his shadow had been on his left, he would be facing north and coming from the south.

Answer: C

D is facing South.

Partners sit opposite each other at a square table, so A faces C and B faces D. C faces west, so C sits on the east side. Facing west, C's right hand points north, so D, on C's right, sits on the north side of the table.

A player on the north side faces the centre of the table, which is towards the south. B, opposite D, sits on the south side facing north, and A sits on the west facing east.

Answer: B

He is North-East of the starting point.

Track the moves on a grid with East as +x and North as +y: 5 m East takes him to (5, 0), 10 m North to (5, 10), and 5 m East to (10, 10).

His final position is 10 m East and 10 m North of the start, so the direction from the starting point is North-East, at a distance of \(10\sqrt{2} \approx 14.1\) m. The fact that his house faces North is a distractor: it says nothing about the direction of his displacement. North-West and South-East point the wrong way on one axis, and plain North ignores the 10 m he went East.

Answer: B

The bank is 25 km from his house.

Add the East-West and North-South moves separately.

\[ \begin{aligned} \text{East} &= 20 + 15 - 20 - 15 = 0 \\ \text{North} &= -5 - 5 + 35 = 25 \end{aligned} \]

The East-West moves cancel, so he ends 25 km due North of the house, and the straight-line distance is 25 km. 35 km is the last northward leg alone, 40 km comes from adding the North-South legs without signs, and 15 km is one of the westward legs.

Answer: C

The friends are 50 m apart.

Take the start as the origin, East as +x and North as +y.

\[ \begin{aligned} A &= (0, 20) \to (-40, 20) \to (-40, 35) \\ B &= (0, -15) \to (10, -15) \to (10, 35) \end{aligned} \]

Both end at the same height, 35 m North of the start, so the distance between them is the horizontal gap \(10 - (-40) = 50\) m. 35 m is their common northward position, and 60 m comes from adding the East-West distances as if both went the same way.

Answer: A

Only one row is correctly matched.

Each pair of perpendicular moves forms a right triangle, so the distance from O is the hypotenuse.

\[ \begin{aligned} \text{Row 1} &: \sqrt{4^2 + 3^2} = 5 \text{ m, South-East} \\ \text{Row 2} &: \sqrt{8^2 + 15^2} = 17 \text{ m, North-West} \\ \text{Row 3} &: \sqrt{6^2 + 8^2} = 10 \text{ m, South-East} \end{aligned} \]

Row 2 is fully right. Row 1 adds the legs (7 m) instead of using Pythagoras and gives East instead of South-East. Row 3 has the distance right but the direction wrong: 6 m South then 8 m East leaves the person South-East of O, not West.

Answer: C

Both 1 and 2 are correct.

Statement 1: the South and East legs are perpendicular, so the distance is

\[ \sqrt{5^2 + 12^2} = \sqrt{169} = 13 \text{ km} \]

Statement 2: measure directions clockwise from North. North-West is 315°; turning 225° clockwise gives \(315 + 225 = 540\), and \(540 - 360 = 180\)°, which is South. Turning 180° from North-West would give South-East, and the extra 45° clockwise brings it to South.

Answer: C

Statement I is true but Statement II is false.

Clockwise from North the directions run North, East, South, West. A 90° clockwise turn from North therefore faces East, so Statement I is true.

Anti-clockwise from North the order is North, West, South, East, so a 90° anti-clockwise turn faces West, not East. Statement II is false.

The options treating both as true miss that the two turns go in opposite senses and so must end in opposite directions.

Answer: B

I am now facing North-east.

Measure directions clockwise from North, so East is 90°.

\[ \begin{aligned} 90 + 100 &= 190^\circ \\ 190 - 145 &= 45^\circ \end{aligned} \]

45° from North is North-east. In net terms the two turns amount to 45° anticlockwise from East. South-west is the exact opposite direction, a 180° error, and North would need a net turn of 90° anticlockwise from East.