Directions: Each of the questions below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; and Give answer (e) if the data in both Statements I and II together are necessary to answer the question. The towns $A$, $B$ and $C$ are on a straight line. Town $C$ is between $A$ and $B$. The distance from $A$ to $B$ is 100 km. How far is $A$ from $C$? (M.B.A., 2003) I. The distance from $A$ to $B$ is 25% more than the distance from $C$ to $B$. II. The distance from $A$ to $C$ is $\frac{1}{4}$ of the distance from $C$ to $B$.

### Concept & Logic When three points lie on a straight line in the sequence $A-C-B$, their segment distances are additive. $$ AC + CB = AB $$ Since we are given that total distance $AB = 100$ km, finding a relational ratio between any two segments will allow us to calculate the exact lengths of all segments. ### Step-by-Step Solution From the main question: $AC + CB = 100$. We need to find $AC$. From Statement I: * Distance $AB$ is 25% more than $CB$. * Mathematically: $AB = 1.25 \times CB$. * Since $AB = 100$, we have $100 = 1.25 \times CB \Rightarrow CB = \frac{100}{1.25} = 80$ km. * Now, $AC = AB - CB = 100 - 80 = 20$ km. * Statement I alone is sufficient. From Statement II: * Distance $AC$ is $\frac{1}{4}$ of $CB$. * Mathematically: $AC = 0.25 \times CB$. * Substitute this into the line equation: $0.25 \times CB + CB = 100 \Rightarrow 1.25 \times CB = 100 \Rightarrow CB = 80$ km. * Thus, $AC = 20$ km. * Statement II alone is sufficient. ### Exam Strategy & Shortcut Both statements give a definitive geometric ratio involving the segments of the line. Since the total segment length is known (100 km), providing ANY definitive ratio between any two parts of that line makes it immediately solvable. You can confidently select "Either" without doing the math. ### Common Pitfall Missing the critical initial context ($C$ is between $A$ and $B$, $AB = 100$) and treating the statements as isolated geometry problems, leading one to falsely assume neither is sufficient on its own. ### Final Answer Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question**.