Direction Sense Test Questions and Answers

Answer: B

Correct answer: 5 km

The two legs are at right angles - east 3 km, then a right turn onto south for 4 km - so the straight-line distance is the hypotenuse: \[ \sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\ \mathrm{km}. \] The 7 km offered is the distance actually travelled along the roads, which is what the phrase “as the crow flies” exists to exclude.

Answer: B

Correct answer: North-West

Track the turns one at a time. He starts south for 5 km, turns right to face west and covers 3 km, turns left to face south again for 4 km, and then goes back - reversing his heading to north - for 10 km. Southward he has gone \( 5+4=9 \) km and northward 10 km, so he ends 1 km north of his start and 3 km west of it. That puts him north-west of the starting place.

Answer: A

Correct answer: North

Walking towards the morning sun means walking east. Turning right takes her south, right again west, and right a third time north.

Answer: A

Correct answer: South

Take the turns in order: north turned 90 degrees clockwise gives east; east turned 180 degrees gives west; west turned 90 degrees anticlockwise gives south.

So he ends up facing south, exactly opposite to his original direction.

Answer: B

Correct answer: 13 miles towards south-west

Take the start as the origin with east and north positive. North 20 gives \( (0,20) \); east 25 gives \( (25,20) \); facing east, a right turn faces south, so 40 gives \( (25,-20) \); another right turn faces west, so 30 gives \( (-5,-20) \); facing west, a left turn faces south, so 12 gives \( (-5,-32) \); and 20 north gives \( (-5,-12) \). The distance is \[ \sqrt{5^2+12^2} = \sqrt{169} = 13\ \mathrm{miles}, \] and being west and south of the origin, the direction is south-west.

Answer: B

Correct answer: South-West

Take P at the origin. Q lies north of P and R east of Q, so R is to the north-east. S lies to P’s left, that is west of P. S is therefore both west of and south of R - to R’s south-west.

Answer: C

the child moves from A to B 90 metres eastwards upto B, then turns right and moves 20 metre upto C, then turns right and moves upto 30 metre upto D. Finally he turns right and moves upto 100 metre upto E.

So AB = 90 metre, BF = CD = 30 metre,
So, AF = AB - BF = 60 metre

Also DE = 100 metre, DF = BC = 20 metre
So, EF = DE - DF = 80 metre

as we can see in image that triangle AFE is a right angled triangle and we are having two sides, need to calculate third one, so we can apply Pythagoras theorem here 

\begin{aligned}
A = AE = \sqrt{AF^2 + EF^2} \\
= \sqrt{(60)^2+(80)^2} \\
= \sqrt{3600+6400} \\
= \sqrt{10000} = 100
\end{aligned}

So from starting point his father was 100 metre away.

Answer: C

Correct answer: 4 km

Resolve the diagonal legs into components, using \( 6/\sqrt{2} = 4.24 \). South-east 6 gives \( (4.24,-4.24) \); west 15 gives \( (-10.76,-4.24) \); north-west 6 adds \( (-4.24,+4.24) \) and gives \( (-15,0) \); east 11 gives \( (-4,0) \). The two diagonal legs are equal and opposite, so they cancel exactly and only the east-west legs survive: \( 15-11 = 4 \) km. Spotting that cancellation removes the need for any arithmetic with surds at all.

Answer: C

Correct answer: 10 km

The south-east and north-west legs are equal and opposite in their north-south parts, so those cancel; both also carry her west, and with the 14 km westward leg she ends 14 km west of the start. The final 4 km back towards the east leaves her \[ 14 - 4 = \mathbf{10}\text{ km} \] away.

Answer: B

Correct answer: South

The sun rises in the east, so shadows at sunrise point towards the west. If west lies to his right, then he must be facing south, since a person facing south has west on the right hand.