Question 1
Five persons X, Y, W, Z and V are to be seated in a row facing North.
The following conditions apply:
- If X sits at an extreme end, then W must sit immediately next to Y
- If X does not sit at an extreme end, then Z must sit at an extreme end
- V 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 W Z V
• X Y W V Z
• W Y V Z X
• Z Y X W V
• V Y X W Z
• V Y W X Z
(shown up to 6)
Step 3: Test each MCQ option
- "X sits at position 3": ✓ Possible in at least one valid arrangement
- "X sits at position 5": ✓ Possible in at least one valid arrangement
- "V sits at position 1": ✓ 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 W Z V
• X Y W V Z
• W Y V Z X
• Z Y X W V
• V Y X W Z
• V Y W X Z
(shown up to 6)
Step 3: Test each MCQ option
- "X sits at position 3": ✓ Possible in at least one valid arrangement
- "X sits at position 5": ✓ Possible in at least one valid arrangement
- "V sits at position 1": ✓ 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.