The question given below consists of two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions. Read all the statements and give answer. Certain number of people are sitting in a row facing north. T sits fourth from the left end. Only one person sits between F and T. How many persons sit in the row? I. S sits fourth to the right of P. Less than three persons sit to the right of S. At least five persons sit between P and the person sitting at the extreme right end. Three persons sit between F and P. At least two persons sit between P and T. II. S is the neighbour of G. There are at least 13 persons in the row. P sits fourth to the right of F. Only two persons sit to the right of S. Only two persons sit between P and G, who is not the neighbour of F. Either one or five persons are there to the left of F.

### Concept & Logic Data Sufficiency in Linear Arrangement. Use given positional constraints to eliminate specific positional cases and determine if a single, unique total number of people can be deduced from either statement independently. ### Step-by-Step Solution **Base Information:** - The row faces North. $T$ sits 4th from the left end (Position 4). - Only 1 person sits between $F$ and $T$. Thus, $F$ can be at Position 2 or 6. **Analyze Statement I:** - Test $F$ at Position 2: We need 3 persons between $F(2)$ and $P$. This forces $P$ to Position 6. Now check the condition "$\ge 2$ persons sit between $P$ and $T$". Between $T(4)$ and $P(6)$ there is only 1 person (Position 5). This violates the condition, so $F$ cannot be 2. - Test $F$ at Position 6: We need 3 persons between $F(6)$ and $P$. $P$ can be at 2 or 10. If $P=2$, only 1 person is between $P(2)$ and $T(4)$, violating the condition. Thus, $P$ must be exactly at Position 10. - $S$ sits 4th to the right of $P$. $10 + 4 = 14$. So, $S$ is at Position 14. - "Less than 3 persons sit to the right of $S$": The total number of people can be 14 (0 right), 15 (1 right), or 16 (2 right). - "At least 5 persons sit between $P$ and the extreme right end": - If total is 14: Between $P(10)$ and right end (14), there are 3 persons (11, 12, 13). Fails. - If total is 15: Between $P(10)$ and right end (15), there are 4 persons. Fails. - If total is 16: Between $P(10)$ and right end (16), there are 5 persons. Satisfies the condition. - The total number of people must uniquely be 16. Statement I alone is sufficient. **Analyze Statement II:** - "Either 1 or 5 persons to the left of $F$" confirms $F$ is at Position 2 or 6. - $P$ sits 4th to the right of $F$, so $P = F + 4$. - 2 persons between $P$ and $G$, and $G$ is not a neighbor of $F$. - Test $F=2, P=6$: $G$ would be 9. $S$ (neighbor of $G$) would be 8 or 10. "Only 2 persons to the right of $S$" means total is $S+2$, which gives 10 or 12. Both violate the "At least 13 persons" rule. - Test $F=6, P=10$: $G$ would be 13 (since $G \neq 5,7$). $S$ is 12 or 14. - If $S=12$, total is 14. (Valid, $\ge 13$). - If $S=14$, total is 16. (Valid, $\ge 13$). - Since the total can be either 14 or 16, Statement II alone is NOT sufficient. ### Exam Strategy & Shortcut In Data Sufficiency, once you establish that a statement yields multiple valid answers (like 14 and 16 in Statement II), stop calculating immediately. Conversely, when intersections of limits (like "$<3$ right of S" and "$\ge 5$ from P") are tight, they almost always force a unique number. ### Common Pitfall Miscalculating the number of people "between" two positions. If you are at position 10 and the end is position 16, there are exactly 5 people between them (11, 12, 13, 14, 15). $16 - 10 - 1 = 5$. Do not just subtract 10 from 16. ### Final Answer Therefore, the correct answer is **Only Statement I is sufficient to answer the question.**