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