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.
Choose the correct answer from the given options.
How many persons sit between T and Y?
Correct Answer :
Three
Solution :
The correct answer is Three.
Let us step-by-step analyze the seating arrangement based on the given clues:
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.
So, the arrangement at this end is either Q - E (facing North, Q is at the left end) or E - Q (Q at the right end). Let's start with Q at the extreme left end: (1) Q, (2) E.
2. Five persons sit between E and T:
Since E is at position 2, moving to the right, five persons sit between E and T.
Positions: Q(1), E(2), _(3), _(4), _(5), _(6), _(7), T(8).
3. K sits immediately to the right of T:
Position of K = 9.
Row so far: Q(1), E(2), _(3), _(4), _(5), _(6), _(7), T(8), K(9).
4. B sits second to the right of K:
Position of B = 11.
Row so far: Q(1), E(2), _(3), _(4), _(5), _(6), _(7), T(8), K(9), _(10), B(11).
5. Two persons sit between K and Y:
K is at 9. Y can be at 9 - 3 = 6 or 9 + 3 = 12.
- If Y is at 6: number of persons between B(11) and Y(6) is 4.
- If Y is at 12: number of persons between B(11) and Y(12) is 0.
Let us test Y at position 12. Then persons between B and Y = 0.
Number of persons between E(2) and H = 2 × 0 = 0. So H is adjacent to E. But position 1 is Q, so H would be at position 3.
Now let's check the number of persons to the left and right of Y:
If Y is at position 12, the number of persons to the left of Y is 11.
The number of persons sitting to the right of Y is four less than the number of persons to the left of Y.
Persons to the right of Y = 11 - 4 = 7.
Total persons in the row = 12 + 7 = 19 (which satisfies "More than twelve persons sit in the row").
6. Count the number of persons between T and Y:
T is at position 8 and Y is at position 12.
The positions between T and Y are 9 (K), 10, and 11 (B).
Therefore, exactly 3 (Three) persons sit between T and Y.
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