M, N, O, P and Q are standing in a row. P is at an end and third to the right of O. N is to the right of Q but left of P. Who is at the left end?
- AM
- BN
- CO
- DP
Solution & Step-by-step Explanation
Let's determine the placement of the 5 individuals step-by-step:
"P is at an end and third to the right of O": This means O must be placed such that moving 3 places to the right reaches P at the extreme right end.
Positions: O, _, _, _, P
"N is to the right of Q but left of P": This tells us the relative order is Q, N, P.
Fitting Q and N into the vacant spaces gives: O, M, Q, N, P or a variation matching the condition. Let's re-verify the "third to the right" constraint:
If O is at index 1, then:
1st right: index 2
2nd right: index 3
3rd right: index 4 (P)
This leaves 5 spots total: O, _, _, P, _. Since P is at an end, P must be at the right-most end of the 5-person row:
Positions: O (1), _ (2), _ (3), P (4) — this only covers 4 positions. Let's fix the 5 positions:
Position: 1, 2, 3, 4, 5
If P is third to the right of O:
Index of P−Index of O=3.
Since P is at an end, let's place P at position 5. Then O must be at position 5−3=2.
Row looks like: _, O, _, _, P.
Now, we have N to the right of Q but left of P. This means Q and N fill positions 3 and 4:
Row becomes: _, O, Q, N, P.
The remaining person M must occupy the extreme left position (Position 1):
Final arrangement: M, O, Q, N, P.
Thus, M is at the left end.
"P is at an end and third to the right of O": This means O must be placed such that moving 3 places to the right reaches P at the extreme right end.
Positions: O, _, _, _, P
"N is to the right of Q but left of P": This tells us the relative order is Q, N, P.
Fitting Q and N into the vacant spaces gives: O, M, Q, N, P or a variation matching the condition. Let's re-verify the "third to the right" constraint:
If O is at index 1, then:
1st right: index 2
2nd right: index 3
3rd right: index 4 (P)
This leaves 5 spots total: O, _, _, P, _. Since P is at an end, P must be at the right-most end of the 5-person row:
Positions: O (1), _ (2), _ (3), P (4) — this only covers 4 positions. Let's fix the 5 positions:
Position: 1, 2, 3, 4, 5
If P is third to the right of O:
Index of P−Index of O=3.
Since P is at an end, let's place P at position 5. Then O must be at position 5−3=2.
Row looks like: _, O, _, _, P.
Now, we have N to the right of Q but left of P. This means Q and N fill positions 3 and 4:
Row becomes: _, O, Q, N, P.
The remaining person M must occupy the extreme left position (Position 1):
Final arrangement: M, O, Q, N, P.
Thus, M is at the left end.