Directions : Study the following information carefully to answer the given…
2022
Directions : Study the following information carefully to answer the given questions:
Two buses P and Q start their journey from bus depot to different destinations. Bus P starts 12km in south and reach at point 1. Then turns left and travel 13km to reach at point 2. Then turns right and travel 14km to reach at point 3. After that it turns left and travels 18km to reach at point 4. Then bus P turns to left and travel 9km to reach final stops 5. Bus Q travel 16km in east of depot to reach at point 6. Now turns right and travel 11km to reach at point 7. Then turns left and travel 22km to reach at point 8. Then turns left and travel 14km to reach at point 9. Finally turns left and travel 39km to reach at point 10.
These stops are assigned names according to the given below conditions:
* If the distance between two consecutive points is prime number, then first stops is called ‘A’
* If the stops (points) are in north-west and south-east of bus depot, then these points are called ‘B’
* If the stops (points) are in north-east of bus depot, then these points are called ‘C’
* If the distance between two consecutive points is even number, then first stops is called ‘D’
Find the odd one out?
- A.
Distance between stop 2 and stop 4
- B.
Distance between stop 7 and stop 9
- C.
Distance between stop 3 and bus depot
- D.
Distance between stop 8 and stop 9
- E.
Distance between stop 6 and bus depot
Show answer & explanation
Correct answer: C
Concept: When two named stops lie on the same bus's route, "the distance between" them is read as the total path length travelled between the two stops — the sum of the intervening leg lengths — not the straight-line displacement; this is the only reading that gives a whole number for every option here (a straight-line distance between two non-adjacent stops on this route is not a whole number). For a sum of whole numbers, an even addend never changes the sum's parity, so a total is odd exactly when it contains an odd COUNT of odd-length legs, and even otherwise (including when it contains zero odd legs).
Application: First list each bus's legs in order.
Bus P: depot → stop 1 = 12 km south; stop 1 → stop 2 = 13 km east; stop 2 → stop 3 = 14 km south; stop 3 → stop 4 = 18 km east; stop 4 → stop 5 = 9 km north.
Bus Q: depot → stop 6 = 16 km east; stop 6 → stop 7 = 11 km south; stop 7 → stop 8 = 22 km east; stop 8 → stop 9 = 14 km north; stop 9 → stop 10 = 39 km west.
Stop 2 to stop 4 = 14 + 18 = 32 km — both legs even, so 0 odd legs → even total.
Stop 7 to stop 9 = 22 + 14 = 36 km — both legs even, so 0 odd legs → even total.
Stop 3 to bus depot = 12 + 13 + 14 = 39 km — exactly one leg (13) is odd, so 1 (odd count) odd leg → odd total.
Stop 8 to stop 9 = 14 km — a single even leg, so 0 odd legs → even total.
Stop 6 to bus depot = 16 km — a single even leg, so 0 odd legs → even total.
Cross-check: Four of the five totals (32, 36, 14, 16) each contain zero odd-length legs and so are even; the stop 3-to-bus-depot path contains exactly one odd-length leg (13 km) and totals 39 km, an odd number — the one that breaks the even pattern shown by every other path.