Six roads lead to a country. They may be indicated by the letters X, Y, Z and…
2023
Six roads lead to a country. They may be indicated by the letters X, Y, Z and the digits 1, 2, 3. When there is a storm, Y is blocked. When there are floods, X, 1 and 2 will be affected and cannot be used. When road 1 is blocked, Z is also blocked. At a time, when there are floods and a storm also blows, which road can be used?
Answer: A. 3 — ConceptIn a condition-elimination problem, collect every item excluded by each condition. Apply direct conditions first, then apply any dependent rule…
- A.
3
- B.
Y
- C.
Z
- D.
More than one of the above
- E.
None of the above
Attempted by 13 students.
Show answer & explanation
Correct answer: A
Concept
In a condition-elimination problem, collect every item excluded by each condition. Apply direct conditions first, then apply any dependent rule triggered by those exclusions. An item that is absent from the final excluded set remains available.
Application
Because the question asks which road can be used during the flood, treat a road described as “affected” by the flood as unavailable in that condition; this makes the flood statement operational for the usability test.
The storm blocks road Y, so the blocked set is {Y}.
Floods affect roads X, 1, and 2, so the blocked set becomes {X, Y, 1, 2}.
Because road 1 is blocked, the dependent rule also blocks road Z; the blocked set is now {X, Y, Z, 1, 2}.
Of the six roads X, Y, Z, 1, 2, and 3, only road 3 is outside the blocked set.
Cross-check
Listing all six roads gives five blocked roads—X, Y, Z, 1, and 2—and one remaining road, 3. Therefore road 3 can be used.