Direction: Read the following information carefully and answer the questions that follow:
There are seven persons namely A, B, C, D, E, F, and G. They all are sitting in a row facing north.
G sits second from one of the ends. E has equal number of persons to his left and right side. F sits on the extreme left end of the row. There are three persons between F and B. A sits immediate right of C. A does not sit at the corner.
How many persons are sitting between A and G?
Correct Answer :
Two
Solution :
The correct answer is Two.
Let's solve the linear arrangement step-by-step based on the given clues:
1. Total Number of Persons:
There are 7 persons (A, B, C, D, E, F, G) sitting in a row, all facing North. Let the 7 positions from left to right be represented as 1, 2, 3, 4, 5, 6, 7.
2. Fixing F's position:
"F sits on the extreme left end of the row."
⇒ Position 1 = F.
3. Fixing B's position:
"There are three persons between F and B."
⇒ Since F is at position 1, B must be at position 5.
Current arrangement: F, _, _, _, B, _, _
4. Fixing E's position:
"E has equal number of persons to his left and right side."
⇒ In a 7-person row, the middle position is position 4.
⇒ Position 4 = E.
Current arrangement: F, _, _, E, B, _, _
5. Fixing G's position:
"G sits second from one of the ends."
⇒ The ends are position 1 and position 7. Second from the left end (position 2) or second from the right end (position 6).
Since position 1 is F, position 2 is vacant. Position 6 is also vacant. However, let's look at the remaining rules for C and A.
6. Fixing C and A's position:
"A sits immediate right of C. A does not sit at the corner."
⇒ C and A must sit together as a pair (C, A).
The vacant spots currently are 2, 3, 6, and 7.
Since A cannot sit at the corner (position 7), the pair (C, A) cannot occupy positions (6, 7).
Therefore, (C, A) must occupy positions 2 and 3 respectively.
⇒ Position 2 = C
⇒ Position 3 = A
7. Completing G and D's positions:
Now, position 2 is occupied by C, so G must be second from the right end.
⇒ Position 6 = G
The only remaining vacant position is position 7, which must be occupied by D.
⇒ Position 7 = D
Final Seating Arrangement (Left to Right):
1: F, 2: C, 3: A, 4: E, 5: B, 6: G, 7: D
Answering the Question:
We need to find the number of persons sitting between A (position 3) and G (position 6).
The persons sitting between A and G are E (position 4) and B (position 5).
Thus, there are exactly Two persons sitting between A and G.
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