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