Next CSE-PPT: 14 March 2027 · Professional & Subprofessional
Civil Service Exam Professional reviewer on direction and distance problems: compass directions, left and right turns, clockwise turns, shadows, and straight-line distances using the Pythagorean theorem.
Direction problems describe a walk in several legs and ask how far, or in which direction, the person ends up from the start. Others describe turns and ask which way the person now faces. Every answer here was computed by a script that traces each path step by step.
Draw the path on scratch paper with north at the top. Cancel opposite movements first (north against south, east against west), then use the Pythagorean theorem on what remains. Turning right is clockwise; turning left is anticlockwise.
Correct answer: D. 5 km
His path forms a right triangle with legs of 3 km and 4 km. By the Pythagorean theorem, the distance is √(3² + 4²) = √25 = 5 km, to the northeast of the start. Adding the legs (7 km) gives the distance walked, not the distance from the start.
Read detailsCorrect answer: D. Southwest
She is south of the start (6 km) and west of it (8 km), so she is to the southwest. Her straight-line distance from the start is √(6² + 8²) = 10 km.
Read detailsCorrect answer: A. 3 km
The 5 km east and 5 km west cancel each other, leaving only the 3 km north. He is 3 km to the north of the start. Draw a quick sketch to see the cancellation.
Read detailsCorrect answer: D. 10 m
Net movement: 10 − 2 = 8 m north and 6 m east. The distance is √(8² + 6²) = √100 = 10 m, to the northeast. Combine opposite directions first, then use the Pythagorean theorem.
Read detailsCorrect answer: A. Southwest
Net movement: 7 − 3 = 4 km west and 4 − 1 = 3 km south. She is to the southwest of the start, 5 km away by the Pythagorean theorem.
Read detailsCorrect answer: D. 13 km
The two legs are 12 km and 5 km, so the distance is √(12² + 5²) = √169 = 13 km, to the northeast. The 5-12-13 right triangle is worth remembering, like 3-4-5.
Read detailsCorrect answer: B. 2 km
North and south cancel (2 − 2 = 0), and east-west gives 3 − 1 = 2 km east. He is 2 km to the east of his starting point.
Read detailsCorrect answer: B. East
Start facing north. A right turn faces east, another right turn faces south, and a left turn from south faces east. She is facing east.
Read detailsCorrect answer: A. North
Clockwise is the same as turning right. From west, two right turns give north and then east; one left turn from east gives north. He is facing north.
Read detailsCorrect answer: D. Northwest
Measure directions clockwise from north: south is 180°. Adding 135° gives 315°, which is northwest (west is 270° and north is 360°). Turning clockwise from south passes through west first.
Read detailsCorrect answer: B. West
In the morning the sun is in the east, so shadows fall towards the west. If Lito faces his shadow, he is facing west, with the sun behind him. In the late afternoon the opposite is true.
Read detailsCorrect answer: A. Northwest
Place the bank at the centre. The post office is east of it, so from the post office you go west to the bank and then north to the library. The library is to the northwest of the post office.
Read detailsCorrect answer: A. 5 km
From Q, go 4 km south to P and then 3 km west to R. The straight-line distance is √(4² + 3²) = 5 km. R is to the southwest of Q.
Read detailsCorrect answer: D. 10 km
The legs of the right triangle are 8 km and 6 km, so the distance is √(64 + 36) = √100 = 10 km. The market is to the northeast of the home.
Read detailsCorrect answer: C. 15 m
Facing east, a left turn faces north and another left turn faces west. The 20 m east and 20 m west cancel, leaving 15 m north. He is 15 m to the north of the start.
Read detailsCorrect answer: C. 15 km
Turning right from north means facing east. The legs are 9 km and 12 km, so the distance is √(81 + 144) = √225 = 15 km, to the northeast.
Read detailsCorrect answer: C. Northwest
Facing south, a right turn faces west, and another right turn faces north. Net movement: 4 km west and 8 − 5 = 3 km north. He is to the northwest of the school, 5 km away.
Read detailsCorrect answer: C. North
From east, a left turn faces north and another left turn faces west. A right turn from west faces north. She is facing north.
Read detailsCorrect answer: A. 40 m
The 30 m west and 30 m east cancel, leaving 40 m north. He is 40 m to the north of the start. The 50 m option wrongly applies the 3-4-5 triangle before cancelling.
Read detailsCorrect answer: B. Northwest
Net movement: 6 − 2 = 4 km west and 5 km north. Since she is both north and west of the start, she is to the northwest. Her distance from the start is √(4² + 5²) = √41 km, about 6.4 km.
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