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