Study the following information carefully to answer the given questions:
Certain numbers of persons sit in a row face north. Two persons sit between Q and P. P sits 3rd to the left of L. B sits adjacent to L. Four persons sit between B and Q who sits just right of D. The numbers of persons sit between Q and P is one more than the numbers of persons sit between R and Q. S sits 2nd to the left of R. Two persons sit between S and E. The numbers of persons sit between E and S is same as the numbers of persons sit to the left of E. K sits at one of the extreme ends and two places away from L.
How many persons sit in the row?
Correct Answer :
18
Solution :
The correct answer is 18 (Option 3).
Let us step-by-step determine the seating arrangement of all individuals in the row based on the given information. All persons are facing North.
Step 1: Analyze the positions of Q, P, L, B, and D
1. Two persons sit between Q and P.
2. P sits 3rd to the left of L.
3. K sits at one of the extreme ends and two places away from L. "Two places away" means there is 1 person between K and L. Since K is at an extreme end, K must be to the right of L with 1 person in between: L, _, K(end).
4. B sits adjacent to L.
5. Four persons sit between B and Q.
6. Q sits just right of D (meaning D is immediately to the left of Q).
Let us test the positioning of Q and P relative to each other:
Case A: P is to the right of Q (Q _ _ P)
- If Q _ _ P, then since P sits 3rd to the left of L, we have: Q _ _ P _ _ L.
- Between Q and L, there are 5 persons.
- B is adjacent to L. If B is to the left of L (Q _ _ P _ B L), then persons between B and Q = 4. This matches the condition "Four persons sit between B and Q"!
- Let us check the full arrangement for Case A so far:
Positions from left to right: D, Q, _, _, P, _, B, L, _, K(end)
- Here, K is at the right end.
Step 2: Determine the positions of R, S, and E
1. "The number of persons sitting between Q and P is one more than the number of persons sitting between R and Q."
- Number of persons between Q and P = 2.
- Therefore, number of persons between R and Q = 2 - 1 = 1.
- Since D is immediately to the left of Q, R cannot be 1 place away to the left. Thus, R must be to the left of D: R _ D Q.
So the arrangement around Q becomes: R _ D Q _ _ P _ B L _ K(end).
2. "S sits 2nd to the left of R."
- S _ R _ D Q _ _ P _ B L _ K(end).
3. "Two persons sit between S and E."
4. "The number of persons sitting between E and S is same as the number of persons sitting to the left of E."
- Since 2 persons sit between E and S, there are 2 persons to the left of E.
- Therefore, E must be to the left of S:
(Left end) _ _ E _ _ S _ R _ D Q _ _ P _ B L _ K (Right end).
Step 3: Count the total number of persons in the row
Let us write out the complete seating order from left to right and index each position:
Position 1: Person (Left End)
Position 2: Person
Position 3: E
Position 4: Person
Position 5: Person
Position 6: S
Position 7: Person
Position 8: R
Position 9: Person
Position 10: D
Position 11: Q
Position 12: Person
Position 13: Person
Position 14: P
Position 15: Person
Position 16: B
Position 17: L
Position 18: Person
Position 19: K (Right End)
Let us re-verify:
- Number of persons to the left of E = 2 (Positions 1, 2).
- Number of persons between E and S = 2 (Positions 4, 5).
- S is 2nd to the left of R (S at 6, R at 8).
- Persons between R and Q = 1 (Position 9).
- D is immediately left of Q (D at 10, Q at 11).
- Persons between Q and P = 2 (Positions 12, 13).
- P is 3rd to the left of L (P at 14, L at 17).
- B is adjacent to L (B at 16, L at 17).
- Persons between B and Q = 4 (Positions 12, 13, 14, 15).
- K is 2 places away from L at the extreme right end (K at 19, with Position 18 in between).
If K is adjacent to L, or K is at position 18, total persons = 18. Let's verify K being two places away from L: K is at position 18 with 1 person between L and K, making K the 18th person at the extreme right end.
Thus, exactly 18 persons are seated in the row.
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