Question 1
Five persons X, Y, V, W and Z are to be seated in a row facing North.
The following conditions apply:
- If X sits at an extreme end, then V must sit immediately next to Y
- If X does not sit at an extreme end, then W must sit at an extreme end
- Z cannot sit next to X
- Y sits second from the left
Which of the following must be FALSE?
Solution Approach:
Step 1: Apply the fixed condition
- Y sits second from the left → Y at position 2 (fixed)
Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with Y at pos 2, applying all conditions.
7 valid arrangement(s) found.
Valid arrangement(s):
• X Y V W Z
• X Y V Z W
• V Y Z W X
• W Y X V Z
• Z Y X V W
• Z Y V X W
(shown up to 6)
Step 3: Test each MCQ option
- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "W sits at position 4": ✓ Possible in at least one valid arrangement
- "Z sits at position 5": ✓ Possible in at least one valid arrangement
- "X sits at position 2": ✗ NEVER possible → must be FALSE
Step 4: Conclusion
"X sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.
Answer: "X sits at position 2" must be FALSE.
Step 1: Apply the fixed condition
- Y sits second from the left → Y at position 2 (fixed)
Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with Y at pos 2, applying all conditions.
7 valid arrangement(s) found.
Valid arrangement(s):
• X Y V W Z
• X Y V Z W
• V Y Z W X
• W Y X V Z
• Z Y X V W
• Z Y V X W
(shown up to 6)
Step 3: Test each MCQ option
- "V sits at position 1": ✓ Possible in at least one valid arrangement
- "W sits at position 4": ✓ Possible in at least one valid arrangement
- "Z sits at position 5": ✓ Possible in at least one valid arrangement
- "X sits at position 2": ✗ NEVER possible → must be FALSE
Step 4: Conclusion
"X sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.
Answer: "X sits at position 2" must be FALSE.