Study the following information carefully and answer the questions given below:
An uncertain number of persons sit in a linear row and face north.
Five persons sit between F and M. D sits third to the right of M. A sits four places away from D. More than four persons sit between A and F. K sits second to the right of A and third from one of the extreme ends of the row. Six persons sit between K and G. E sits fifth to the left of G. E sits fourth from one of the extreme ends of the row. As many persons sits to the left of E as to the right of H.
Who sits eighth to the left of H?
Correct Answer :
M
Solution :
To find the correct answer, let us analyze and reconstruct the linear seating arrangement step-by-step based on the given clues.
Clue 1: An uncertain number of persons sit in a linear row and face north.
Clue 2: E sits fourth from one of the extreme ends of the row. This gives two possibilities for E:
Case 1: E is fourth from the left end. (i.e., [Left End] _ _ _ E ...)
Case 2: E is fourth from the right end. (i.e., ... E _ _ _ [Right End])
Clue 3: E sits fifth to the left of G. This means there are 4 persons between E and G, and G is to the right of E:
E _ _ _ _ G
Clue 4: Six persons sit between K and G. This means K can be either to the left of G or to the right of G.
Let us test the positioning:
If E is 4th from the left end (Case 1):
The arrangement starts as: 1 2 3 E 5 6 7 8 G
If K is to the left of G with 6 persons between them: G is at position 9. Six persons between K and G means K is at position 9 - 7 = 2. But we are given that "K sits third from one of the extreme ends of the row." If K is at position 2 from the left, it is second from the end, not third. So K cannot be to the left of G in this case.
If K is to the right of G with 6 persons between them: K is at position 9 + 7 = 16. For K to be third from the right end, the row must end at position 18. Let's check this layout:
Positions: 1 2 3 E(4) 5 6 7 8 G(9) 10 11 12 13 14 15 K(16) 17 18(Right End).
Here, K is indeed 3rd from the right end. Let's proceed with this configuration.
Clue 5: K sits second to the right of A. This means A sits second to the left of K:
A _ K.
So, A is at position 16 - 2 = 14.
Clue 6: A sits four places away from D. "Four places away" means there are 3 persons between A and D. Thus, D can be either to the left of A (position 14 - 4 = 10) or to the right of A (position 14 + 4 = 18).
If D is at position 18, it would be the right end of the row. Let's check: D sits third to the right of M. This means M is at position 18 - 3 = 15.
If M is at position 15, then: Five persons sit between F and M. F could be at position 15 - 6 = 9, or position 15 + 6 = 21.
But G is already at position 9, so F cannot be at position 9. If F is at position 21, the row would need to extend beyond 18, which contradicts K being third from the right end (position 16 in a row of 18). Therefore, D must be to the left of A.
So, D is at position 14 - 4 = 10.
Clue 7: D sits third to the right of M. This means M is at position 10 - 3 = 7.
Clue 8: Five persons sit between F and M. This means F can be at position 7 - 6 = 1, or position 7 + 6 = 13.
We are also given: "More than four persons sit between A and F."
If F is at position 13: The number of persons between A(14) and F(13) is 0, which is not more than four.
If F is at position 1: The number of persons between A(14) and F(1) is 14 - 1 - 1 = 12, which is more than four. This satisfies the condition. Thus, F is at position 1.
Clue 9: As many persons sit to the left of E as to the right of H.
Since E is at position 4, there are 3 persons sitting to the left of E (at positions 1, 2, and 3).
Therefore, there must be exactly 3 persons sitting to the right of H. This means H must be fourth from the right end of the row (position 18 - 3 = 15).
So, H is at position 15.
Let us write down the full seating arrangement from position 1 to 18:
1: F
2: _
3: _
4: E
5: _
6: _
7: M
8: _
9: G
10: D
11: _
12: _
13: _
14: A
15: H
16: K
17: _
18: _
Question: Who sits eighth to the left of H?
Since H is at position 15, the person sitting eighth to the left of H is at position:
15 - 8 = 7.
Looking at our seating arrangement, position 7 is occupied by M.
Thus, M sits eighth to the left of H.
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