Seven persons A, B, C, D, E, F and G sit in a row facing north. They have different elements named copper, nickel, gold, mercury, aluminum, silver and iron. The information is not used in the same order as given. The one who have gold sits third to the left of D, none of them sits at any of the extreme ends. E sits immediate right of the one who have gold. B and E sit adjacent to each other. The one who have iron sits second to the left of B. Two persons sit between G and F. The one who has mercury sits fourth to the right of G. The one who have copper sits immediate right of the one who has silver. The one who have nickel sits to the left of F and to the right of A.
Choose the correct combination.
Correct Answer :
E - Silver
Solution :
To determine the correct combination, let us systematically analyze the clues and construct the seating arrangement for the seven persons (A, B, C, D, E, F, and G) sitting in a row facing north (from left to right, positions 1 to 7).
Let the positions be numbered 1, 2, 3, 4, 5, 6, and 7 from left to right.
Clue 1: "The one who have gold sits third to the left of D, none of them sits at any of the extreme ends."
This means neither the person with gold nor D sits at position 1 or 7. Let's denote the position of the person with gold as g and the position of D as d.
Since the one with gold is third to the left of D, we have:
or .
Since and , the possible positions for are:
Case A: and
Case B: and
Clue 2: "E sits immediate right of the one who have gold."
So, the position of E is .
In Case A (): E is at position 3.
In Case B (): E is at position 4.
Clue 3: "B and E sit adjacent to each other."
So B's position can be or .
Since the person with gold is at , and we do not yet know if B has gold, let's keep both options open.
Clue 4: "The one who have iron sits second to the left of B."
This means B's position minus 2 must be a valid position (at least 1). So B cannot be at position 2.
Let's analyze Case A (, E at 3):
Since B is adjacent to E, B could be at position 2 or 4. But B cannot be at 2 (since the person second to the left of B would be at 0, which is invalid). Thus, B must be at position 4.
The one who has iron sits second to the left of B (position 4 - 2 = 2). So the person at position 2 (who has gold) must also have iron, which is a contradiction because each person has a different element. Thus, Case A is eliminated.
Let's analyze Case B (, D at 6, E at 4):
Since B is adjacent to E (position 4), B can be at position 3 or 5.
- If B is at position 3: The one who has iron is at position 1 (3 - 2 = 1). This is possible.
- If B is at position 5: The one who has iron is at position 3 (5 - 2 = 3). But position 3 has gold. This is a contradiction since a person cannot have both gold and iron. Thus, B must be at position 3, and the person at position 1 has iron.
So far, we have the following arrangement:
Position 1: [Iron]
Position 2: [ ]
Position 3: B [Gold]
Position 4: E [ ]
Position 5: [ ]
Position 6: D [ ]
Position 7: [ ]
Clue 5: "Two persons sit between G and F" and "The one who has mercury sits fourth to the right of G."
Since the one with mercury sits fourth to the right of G, G's position must be at most 3 ().
- If G is at 1: The one with mercury is at 5 (). Since two persons sit between G and F, F must be at 4. But E is already at position 4. So G cannot be at 1.
- If G is at 2: The one with mercury is at 6 (). Since two persons sit between G and F, F must be at 5. This is possible.
- If G is at 3: Position 3 is already occupied by B. So G cannot be at 3.
Thus, G is at position 2, F is at position 5, and the person at position 6 (D) has mercury.
Let's update our arrangement:
Position 1: [Iron]
Position 2: G [ ]
Position 3: B [Gold]
Position 4: E [ ]
Position 5: F [ ]
Position 6: D [Mercury]
Position 7: [ ]
Clue 6: "The one who have copper sits immediate right of the one who has silver."
This means silver and copper must be in adjacent positions, with silver on the left and copper on the right (Silver, Copper).
Looking at the available vacant element spots: Position 2, Position 4, Position 5, Position 7.
The consecutive vacant element slots are (2, 4) - not adjacent, (4, 5) - adjacent, and (5, 7) - not adjacent.
Therefore, Silver must be at position 4 (E) and Copper must be at position 5 (F).
This gives: E has Silver, and F has Copper.
Clue 7: "The one who have nickel sits to the left of F and to the right of A."
Since F is at 5, the one with nickel must be to the left of 5 (positions 1, 2, 3, or 4). We know the elements for 1 (Iron), 3 (Gold), and 4 (Silver) are already determined, so the one with nickel must be at position 2 (G).
G (Nickel) sits to the right of A. Since G is at 2, A must be to the left of G, which means A is at position 1.
The remaining person C must be at position 7. The remaining element aluminum must be at position 7 (C).
Final Arrangement:
Position 1: A - Iron
Position 2: G - Nickel
Position 3: B - Gold
Position 4: E - Silver
Position 5: F - Copper
Position 6: D - Mercury
Position 7: C - Aluminum
Comparing our final arrangement with the options:
- A - Nickel (Incorrect, A has Iron)
- E - Silver (Correct)
- D - Copper (Incorrect, D has Mercury)
- C - Mercury (Incorrect, C has Aluminum)
Therefore, the correct combination is E - Silver.
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