Five planes, A, B, P, Q and R were saluting on Independence Day in such a way that R was second to the left of Q but to the immediate right of A. There was one plane between B and P. B was not at any of the ends. P and Q were neighbours. Who was at the left end?
- AA
- BB
- CR
- DQ
Solution & Step-by-step Explanation
Let's determine the placement positions from left to right based on the conditions given:
"R was second to the left of Q": This means the arrangement looks like R_Q.
"...but [R was] to the immediate right of A": This means A is placed right next to the left of R, giving the configuration: A R_Q.
"P and Q were neighbours": Since Q has an empty spot to its left, P must fill that intermediate space, yielding: A R P Q.
"There was one plane between B and P": Since P is at the third spot from the left, B can be positioned at the far right end to satisfy this layout (A R P Q B). However, the statement specifies: "B was not at any of the ends".
Let us reconsider the placement of P and Q being neighbours. P can be to the right of Q. Let's re-verify:
If the arrangement is A R B P Q:
R is second to the left of Q? Yes, position of R is 2nd, position of Q is 5th (which is third to the left, so incorrect).
Let's carefully layout the 5 positions: _____
R is second to the left of Q →RXQ.
R is to the immediate right of A →ARXQ.
Since there are 5 planes, the remaining plane must be either at the left or right end. So the arrangement is either Y A R X Q or A R X Q Y.
Case 1: Y A R X Q
The remaining elements to place are B and P.
"P and Q are neighbours" →X must be P. So we get Y A R P Q.
Then Y must be B, giving B A R P Q. But "B was not at any of the ends", so this case is rejected.
Case 2: A R X Q Y
"P and Q are neighbours" →P can be either X or Y.
If X=P, the arrangement is A R P Q B (since Y=B). But B cannot be at the end. So this is also invalid.
If Y=P, the arrangement is A R B Q P (since X=B).
Let's check all constraints for A R B Q P:
R is second to the left of Q? Positions: A(1),R(2),B(3),Q(4),P(5). Yes, R is second to the left of Q.
R is to the immediate right of A? Yes.
There was one plane between B and P? Yes, Q is between B and P.
B was not at any of the ends? Yes, B is at position 3.
P and Q were neighbours? Yes, positions 4 and 5.
Everything matches. The final linear alignment from left to right is: A, R, B, Q, P.
Thus, A is at the extreme left end.
"R was second to the left of Q": This means the arrangement looks like R_Q.
"...but [R was] to the immediate right of A": This means A is placed right next to the left of R, giving the configuration: A R_Q.
"P and Q were neighbours": Since Q has an empty spot to its left, P must fill that intermediate space, yielding: A R P Q.
"There was one plane between B and P": Since P is at the third spot from the left, B can be positioned at the far right end to satisfy this layout (A R P Q B). However, the statement specifies: "B was not at any of the ends".
Let us reconsider the placement of P and Q being neighbours. P can be to the right of Q. Let's re-verify:
If the arrangement is A R B P Q:
R is second to the left of Q? Yes, position of R is 2nd, position of Q is 5th (which is third to the left, so incorrect).
Let's carefully layout the 5 positions: _____
R is second to the left of Q →RXQ.
R is to the immediate right of A →ARXQ.
Since there are 5 planes, the remaining plane must be either at the left or right end. So the arrangement is either Y A R X Q or A R X Q Y.
Case 1: Y A R X Q
The remaining elements to place are B and P.
"P and Q are neighbours" →X must be P. So we get Y A R P Q.
Then Y must be B, giving B A R P Q. But "B was not at any of the ends", so this case is rejected.
Case 2: A R X Q Y
"P and Q are neighbours" →P can be either X or Y.
If X=P, the arrangement is A R P Q B (since Y=B). But B cannot be at the end. So this is also invalid.
If Y=P, the arrangement is A R B Q P (since X=B).
Let's check all constraints for A R B Q P:
R is second to the left of Q? Positions: A(1),R(2),B(3),Q(4),P(5). Yes, R is second to the left of Q.
R is to the immediate right of A? Yes.
There was one plane between B and P? Yes, Q is between B and P.
B was not at any of the ends? Yes, B is at position 3.
P and Q were neighbours? Yes, positions 4 and 5.
Everything matches. The final linear alignment from left to right is: A, R, B, Q, P.
Thus, A is at the extreme left end.