Question 1
Five persons Y, V, Z, X and W are to be seated in a row facing North.
The following conditions apply:
- If Y sits at an extreme end, then Z must sit immediately next to V
- If Y does not sit at an extreme end, then X must sit at an extreme end
- W cannot sit next to Y
- 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):
• Y V Z X W
• Y V Z W X
• Z V W X Y
• X V Y Z W
• W V Y Z X
• W V Z Y X
(shown up to 6)
Step 3: Test each MCQ option
- "X sits at position 4": ✓ Possible in at least one valid arrangement
- "W sits at position 5": ✓ Possible in at least one valid arrangement
- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "Y sits at position 4": ✓ Possible in at least one valid arrangement
Step 4: Conclusion
"Y 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: "Y 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):
• Y V Z X W
• Y V Z W X
• Z V W X Y
• X V Y Z W
• W V Y Z X
• W V Z Y X
(shown up to 6)
Step 3: Test each MCQ option
- "X sits at position 4": ✓ Possible in at least one valid arrangement
- "W sits at position 5": ✓ Possible in at least one valid arrangement
- "Y sits at position 2": ✗ NEVER possible → must be FALSE
- "Y sits at position 4": ✓ Possible in at least one valid arrangement
Step 4: Conclusion
"Y 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: "Y sits at position 2" must be FALSE.