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.
The number of persons sitting between K and Y is twice the number of persons sitting between ____ and _____.
Correct Answer :
K, B
Solution :
The correct answer is K, B.
Step-by-step Explanation:
Let us determine the seating arrangement step-by-step according to the given information, assuming all persons are facing North:
1. Position of Q and E:
"E is the only neighbor of Q."
This implies Q must be sitting at one of the extreme ends of the row. Placing Q at the extreme left end (Position 1) means E sits at Position 2.
2. Position of T:
"Five persons sit between E and T."
Since E is at Position 2, the 5 persons sit in Positions 3, 4, 5, 6, and 7. Therefore, T sits at Position 8.
3. Position of K:
"K sits immediately to the right of T."
Since T is at Position 8, K sits at Position 9.
4. Position of B:
"B sits second to the right of K."
Since K is at Position 9, B sits at Position 11.
5. Position of Y:
"Two persons sit between K and Y."
Since K is at Position 9 and B is at Position 11, placing Y to the right of K puts Y at Position 12 (with Positions 10 and 11 sitting between K and Y).
6. Position of H:
"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 between B (Position 11) and Y (Position 12) is 0.
Therefore, the number of persons between E and H is 2 × 0 = 0. This means H sits immediately next to E at Position 3.
7. Total Number of Persons:
"The number of persons sitting to the right of Y is four less than the number of persons sitting to the left of Y."
The number of persons to the left of Y (Positions 1 to 11) is 11.
So, the number of persons to the right of Y is 11 - 4 = 7.
Total persons in the row = 12 + 7 = 19 (which satisfies the condition that more than twelve persons sit in the row).
Summary of Positions:
- Position 1: Q
- Position 2: E
- Position 3: H
- Position 8: T
- Position 9: K
- Position 11: B
- Position 12: Y
Evaluation of Question:
- The number of persons sitting between K and Y is 2.
- We need to find two persons between whom the number of sitting persons is 1 (since 2 is twice of 1).
- Between K (Position 9) and B (Position 11), there is exactly 1 person sitting (Position 10).
Therefore, the number of persons sitting between K and Y is twice the number of persons sitting between K, B.
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