Directions: Study the following information carefully and answer the question.…
2024
Directions: Study the following information carefully and answer the question.
In a certain coded language:
M@6N means M is 4 m north of N.
M%9N means M is 6 m south of N.
M#4N means M is 2 m east of N.
M$5N means M is 2 m west of N.
Conditions: A%8B, C$12B, Z#17D, E$19F, C%11E, Z@9F, G%4D, A$7R, R%14W
If G#4S, what is the total distance from S to B along the connected path S–G–D–Z–F–E–C–B?
Answer: D. 58m — ConceptIn coded-direction problems, first translate each symbol into a direction and its number into the stated distance rule. A total route distance is the…
- A.
47m
- B.
57m
- C.
48m
- D.
58m
- E.
60m
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Concept
In coded-direction problems, first translate each symbol into a direction and its number into the stated distance rule. A total route distance is the sum of the lengths of every consecutive segment on the specified path; direction affects placement, not segment length.
Application
From G#4S, the # rule gives 4 − 2 = 2 m, so S–G = 2 m.
From G%4D, the % rule gives 4 − 3 = 1 m, so G–D = 1 m.
From Z#17D, the # rule gives 17 − 2 = 15 m, so D–Z = 15 m.
From Z@9F, the @ rule gives 9 − 2 = 7 m, so Z–F = 7 m.
From E$19F, the $ rule gives 19 − 3 = 16 m, so F–E = 16 m.
From C%11E, the % rule gives 11 − 3 = 8 m, so E–C = 8 m.
From C$12B, the $ rule gives 12 − 3 = 9 m, so C–B = 9 m.
Add the seven consecutive segments: 2 + 1 + 15 + 7 + 16 + 8 + 9 = 58 m.
Cross-check
Regrouping the same route gives horizontal travel 2 + 15 + 16 + 9 = 42 m and vertical travel 1 + 7 + 8 = 16 m. Their sum is 42 + 16 = 58 m, confirming the route total.
Therefore, the total distance from S to B along the connected path is 58 m.