Question Details

Read the given information carefully and answer the questions given below:

14 persons sit in two parallel rows containing seven persons in each row. A, B, C, D, E, F and G – sit in row 1 and face north while P, Q, R, S, T, U and V – sit in row 2 and face south. But not necessarily in the same order. Persons of row 1 face the persons of row 2.

Three persons sit between B and D. D sits at one of the ends. Two persons sit between Q and the one who faces B. One person sits between Q and T. U sits fourth to the right of S but does not sit opposite to D. One person sits between A and the one who faces S. G sits immediate right of C. P does not face C. Number of persons sit to the right of F and V are equal.

If the persons of row 1 are made to sit in alphabetical order from left, then who will remain at his previous position?

Options

A

Only B and F

B

Only F

C

Only A

D

Only B and E

Show Answer

Correct Answer :

Option B

Only F

Only F

Solution :

To determine who will remain at their previous position when Row 1 is arranged in alphabetical order from left to right, we first need to determine the final seating arrangement of both rows from the given clues.

Row 1 contains seven persons: A, B, C, D, E, F, and G, all facing North (Left to Right is West to East).
Row 2 contains seven persons: P, Q, R, S, T, U, and V, all facing South (Left to Right is East to West, so their right is towards the West, which is the left side of Row 1).

Let's represent the seven positions from left to right as 1, 2, 3, 4, 5, 6, 7.

Step 1: Position B and D.
"Three persons sit between B and D. D sits at one of the ends."
This gives us two cases:
Case 1: D is at position 1. Then B must be at position 5 (since 2, 3, and 4 sit between them).
Case 2: D is at position 7. Then B must be at position 3 (since 4, 5, and 6 sit between them).

Step 2: Position Q and T.
"Two persons sit between Q and the one who faces B. One person sits between Q and T."
In Case 1: B is at position 5. The person facing B is at position 5 of Row 2. Q sits two persons away from position 5, so Q must be at position 2 of Row 2.
Since one person sits between Q and T, T must be at position 4 of Row 2.
In Case 2: B is at position 3. The person facing B is at position 3 of Row 2. Q sits two persons away from position 3, so Q must be at position 6 of Row 2.
Since one person sits between Q and T, T must be at position 4 of Row 2.

Step 3: Position U and S.
"U sits fourth to the right of S but does not sit opposite to D."
Since Row 2 faces South, their right is to our left (towards position 1). Thus, U is 4 places to the left of S, meaning S sits at some position and U is at (position of S - 4).
The possible pairs for (U, S) are:
- If S is at position 5, U is at position 1.
- If S is at position 6, U is at position 2.
- If S is at position 7, U is at position 3.
Let's test these under our cases:
In Case 1:
D is at position 1. Therefore, U cannot be at position 1 (since U does not sit opposite to D).
In Row 2, Q is at 2 and T is at 4. If S is at position 6, U is at position 2 (which is occupied by Q - invalid).
If S is at position 7, U is at position 3 (available). So in Case 1, U is at position 3, and S is at position 7.
In Case 2:
D is at position 7. Therefore, U cannot be at position 7. In Row 2, Q is at 6 and T is at 4.
If S is at position 5, U is at position 1 (available). So U is at position 1, and S is at position 5.
If S is at position 7, U is at position 3 (available). But if U is at position 3, S is at position 7, which faces D (which is allowed since U does not face D, but let's look at other clues to see which case is valid).

Step 4: Position A.
"One person sits between A and the one who faces S."
In Case 1: S is at position 7. The person facing S is at position 7. One person sits between A and position 7, so A must be at position 5. But position 5 is occupied by B. This makes Case 1 invalid.

Let's re-evaluate Case 2:
In Row 1: B is at position 3, D is at position 7.
In Row 2: T is at 4, Q is at 6.
Subcase 2a: S is at position 5, U is at position 1.
The person facing S is at position 5. One person sits between A and position 5, so A must be at position 3. But position 3 is occupied by B. Thus, Subcase 2a is invalid.
Subcase 2b: S is at position 7, U is at position 3.
The person facing S is at position 7 (which is D). One person sits between A and D (position 7), so A must be at position 5. This is valid.

So, the arrangement so far for Subcase 2b is:
Row 1: _ , _ , B , _ , A , _ , D
Row 2: _ , _ , U , T , _ , Q , S

Step 5: Position G and C.
"G sits immediate right of C." (Since they face North, G is to the immediate right of C, so we have the block 'CG' in consecutive positions).
Looking at Row 1: The empty positions are 1, 2, and 6. The only adjacent empty slots are 1 and 2. Therefore, C must be at position 1, and G must be at position 2.
Row 1 now becomes: C, G, B, _ , A, _ , D

Step 6: Remaining positions.
"P does not face C."
C is at position 1. Thus, P cannot be at position 1 of Row 2.
The remaining empty positions in Row 2 are 2 and 5.
Since P cannot be at position 1, let's see where P can go. P must go to position 2 or 5. Let's look at the next clue first.
"Number of persons sit to the right of F and V are equal."
In Row 1, the remaining positions are 4 and 6. One of them is F, and the other is E.
In Row 2, the remaining positions are 2 and 5 (for P and V).
Since V faces South, the number of persons to the right of V (which is to the left in the diagram, towards position 1) is x.
Since F faces North, the number of persons to the right of F (which is to the right in the diagram, towards position 7) is also x.
Let's test the possibilities:
If F is at position 4: Persons to the right of F = 3 (positions 5, 6, 7).
Then V must have 3 persons to its right in Row 2. Since Row 2 faces South, the right side is towards position 1. So V must be at position 4. But position 4 of Row 2 is occupied by T. Thus, F cannot be at position 4.
If F is at position 6: Persons to the right of F = 1 (position 7).
Then V must have 1 person to its right in Row 2. The position with 1 person to its right (towards position 1) is position 2. So V is at position 2. This is valid! All other positions match.
Therefore:
F is at position 6, which leaves E at position 4.
V is at position 2, which leaves P at position 5.
Let's check if P faces C: C is at position 1, P is at position 5. Indeed, P does not face C.

Final Seating Arrangement for Row 1:
1: C
2: G
3: B
4: E
5: A
6: F
7: D

Step 7: Arrange Row 1 in alphabetical order from left to right.
Alphabetical order of A, B, C, D, E, F, G is:
1: A
2: B
3: C
4: D
5: E
6: F
7: G

Comparing the previous positions with the new alphabetical positions:
- Position 1: C → A (Changed)
- Position 2: G → B (Changed)
- Position 3: B → C (Changed)
- Position 4: E → D (Changed)
- Position 5: A → E (Changed)
- Position 6: F → F (Remained Same)
- Position 7: D → G (Changed)

Thus, only F remains at his previous position.

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