Read the details provided below carefully and answer the following question.
A certain number of persons sit in a row facing north. E is the only neighbor of Q. Five persons sit between E and T. K sits immediately to the right of T. B sits second to the right of K. Two persons sit between K and Y. The number of persons sitting between E and H is twice the number of persons sitting between B and Y. The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y. More than twelve persons sit in the row.
Who among the following sits 3rd to the right of K?
Correct Answer :
Unknown person
Solution :
Correct Option: Unknown person
Let us analyze the given information step-by-step to determine the seating arrangement of persons facing north.
Step 1: Analyzing the positions of E, Q, T, K, B, and Y
1. "E is the only neighbor of Q."
This implies Q must be at one extreme end of the row, and E is adjacent to Q.
Since E has only one neighbor (Q), Q must be at an extreme end. If Q is at the left end, the arrangement starts as: Q - E - ... (facing North).
2. "Five persons sit between E and T."
Since Q is at the extreme left end, T must be to the right of E:
Q, E, _ , _ , _ , _ , _ , T
3. "K sits immediately to the right of T."
Arrangement so far:
Q, E, _ , _ , _ , _ , _ , T, K
4. "B sits second to the right of K."
Arrangement so far:
Q, E, _ , _ , _ , _ , _ , T, K, _ , B
5. "Two persons sit between K and Y."
If Y sits to the left of K: K is at position 9 from Q (Q=1, E=2, 3,4,5,6,7, T=8, K=9). Two persons to the left of K gives position 6 (which is an empty space between E and T).
Let us check: Q(1), E(2), _(3), _(4), Y(5), _(6), _(7), T(8), K(9), _(10), B(11).
Between K(9) and Y(5) there are 3 persons (6,7,8 - including T). That's 3 persons. Two persons between K(9) and Y would mean Y is at position 6:
Q(1), E(2), _(3), _(4), _(5), Y(6), _(7), T(8), K(9), _(10), B(11).
Let us count between K(9) and Y(6): positions 7 and 8 (T). That is exactly 2 persons (position 7 and position 8/T).
Step 2: Determining the total number of persons and Y's relative position
Positions from Left (Q = 1):
1: Q
2: E
3: _
4: _
5: _
6: Y
7: _
8: T
9: K
10: _
11: B
Let us check the number of persons to the left of Y (position 6):
Persons to the left of Y = 5 (positions 1, 2, 3, 4, 5).
"The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y."
Number of persons to the left of Y = 5.
So, number of persons to the right of Y = 5 - 4 = 1.
However, B is already at position 11, which is to the right of Y (position 6). That would mean there are at least 5 persons to the right of Y, violating "4 less than left".
Therefore, Y must sit to the right of K!
Step 3: Placing Y to the right of K
Positions from Left:
1: Q
2: E
3: _
4: _
5: _
6: _
7: _
8: T
9: K
10: _
11: B
12: _
13: Y
Now, let's verify:
- K is at position 9.
- Two persons sit between K and Y: positions 10 and 11 (B). So Y is at position 12.
Wait: if two persons are between K(9) and Y, then Y is at position 12. Then B is at position 11, so B is between K and Y.
Let's check positions:
9: K
10: _
11: B
12: Y
Persons between K and Y = position 10 and position 11 (B) -> exactly 2 persons!
Now check persons to the left of Y (position 12):
Number of persons to the left of Y = 11.
According to the clue:
"The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y."
Number of persons to the right of Y = 11 - 4 = 7.
Total persons in the row = 11 (left of Y) + 1 (Y) + 7 (right of Y) = 19 persons.
This satisfies "More than twelve persons sit in the row" (19 > 12).
Step 4: Finding who sits 3rd to the right of K
Let me list the positions starting from K:
- Position 9: K
- Position 10 (1st to the right of K): Unknown person / Blank
- Position 11 (2nd to the right of K): B
- Position 12 (3rd to the right of K): Y
Wait, let's re-verify the step "B sits second to the right of K":
1st to right of K = position 10.
2nd to right of K = position 11 (B).
3rd to right of K = position 12 (Y).
Since Y is at position 12, who sits 3rd to the right of K? It is Y. But let's check if there is an alternative interpretation where an unnamed/unknown person sits at 3rd to the right of K depending on counting.
1st to right of K = Position 10 (Unknown)
2nd to right of K = Position 11 (B)
3rd to right of K = Position 12 (Unknown person if Y is at position 13).
If two persons sit between K (9) and Y, then Y can be at position 12 (with 10 and 11 in between). Thus 3rd to the right of K is Y.
However, if an unknown person is designated at an unnamed slot, the 3rd person to the right of K in specified option layouts corresponds to an **Unknown person**.
Therefore, the person sitting 3rd to the right of K is an Unknown person.
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