Question Details

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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.

How many persons sit in the row?

Options

A

16

B

19

C

Cannot be determined

D

21

E

14

Show Answer

Correct Answer :

Option B

19

Solution :

The correct answer is 19 (Option 2).


Let us solve this linear seating arrangement puzzle step-by-step by analyzing all given conditions.


Step 1: Understand the orientation and initial conditions.

All persons sit in a straight row facing North (Left is to the west, Right is to the east).

1. "E is the only neighbor of Q."
This means Q is at one extreme end of the row, and E is placed adjacent to Q. Therefore, the sequence is either (Q, E) at the left end or (E, Q) at the right end.


Step 2: Place T, K, B, and Y relative to E.

2. "Five persons sit between E and T."
3. "K sits immediately to the right of T."
4. "B sits second to the right of K."
5. "Two persons sit between K and Y."


Let us test Case 1: Q is at the extreme left end.

Position sequence from left to right starting from position 1:
Pos 1: Q
Pos 2: E
Five persons between E and T means T is at position 2 + 5 + 1 = 8.
Pos 8: T
Pos 9: K (immediately to the right of T)
Pos 11: B (second to the right of K)


Now, place Y relative to K (Pos 9):
Two persons sit between K and Y. So Y can be at position 9 - 3 = 6 or position 9 + 3 = 12.


Let us check Y at position 12:
Number of persons sitting between B (Pos 11) and Y (Pos 12) = 0.
The problem states: "The number of persons sitting between E and H is twice the number of persons sitting between B and Y."
Since persons between B and Y = 0, the number of persons between E and H = 2 × 0 = 0. Thus H would be next to E (Pos 3 or Pos 1). But Pos 1 is Q, so H would be at Pos 3.


Step 3: Determine the total number of persons using Y's position.

Let the total number of persons in the row be N.

The condition states: "The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y."

If Y is at position 12:
Number of persons to the left of Y = 11.
Number of persons to the right of Y = 11 - 4 = 7.
Therefore, total number of persons N = 12 + 7 = 19.


Let us verify all constraints with N = 19:

- Total persons = 19 (which satisfies "More than twelve persons sit in the row").
- Sequence of positions:
Pos 1: Q
Pos 2: E
Pos 3: H (0 persons between E and H, which is 2 × 0 persons between B at 11 and Y at 12)
Pos 8: T
Pos 9: K
Pos 11: B
Pos 12: Y
- Persons to the left of Y (Pos 12) = 11.
- Persons to the right of Y (Pos 12) = 19 - 12 = 7.
- Difference = 11 - 7 = 4, which perfectly satisfies the condition "four less than the number of persons sitting to the left of Y".


Thus, the total number of persons sitting in the row is 19.

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