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.

Step 1: Determine the positions of Q, E, T, K, and B.
All persons sit facing North.
"E is the only neighbor of Q": This means Q must sit at an extreme end of the row.
Case 1: Place Q at the extreme left end (Position 1). Since E is Q's only neighbor, E sits at Position 2.
"Five persons sit between E and T": Counting 5 positions to the right of E (positions 3, 4, 5, 6, 7), T sits at Position 8.
"K sits immediately to the right of T": K sits at Position 9.
"B sits second to the right of K": B sits at Position 11.

Step 2: Determine the position of Y.
"Two persons sit between K and Y": K is at Position 9. If Y were placed to the left of K (Position 6), the total number of persons in the row would be less than 12, violating the condition that more than twelve persons sit in the row. Thus, Y must sit to the right of K.
Placing 2 persons (Position 10 and Position 11/B) between K (Position 9) and Y places Y at Position 12.

Step 3: Determine the position of H.
The number of persons sitting between B (Position 11) and Y (Position 12) is 0.
"The number of persons sitting between E and H is twice the number of persons sitting between B and Y":
Number of persons between E and H = 2 × 0 = 0.
Therefore, H sits immediately next to E. Since Position 1 is occupied by Q and Position 2 by E, H must sit at Position 3.

Step 4: Calculate the total number of persons in the row.
Y is at Position 12, which means there are 11 persons sitting to the left of 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":
Number of persons to the right of Y = 11 - 4 = 7 persons.


Total persons=11+1+7=19

Since 19 is greater than 12, this seating arrangement satisfies all given constraints. Hence, there are 19 persons sitting in the row.

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