Question

A car drives along a straight road from place S to place L passing through F along the way. What is the total distance travelled by car from S to L? Statement (I): Distance from S to F is \(\frac{3}{5}\) of the distance from S to L.
Statement (II): Distance from F to L is 12 km.

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

Always express the partial segments in terms of the total distance \( D \) to create a solvable algebraic equation.

Answer 1

The Correct Option is C

Concept: The total distance from S to L, denoted as \( D \), is composed of two segments, SF and FL, because point F lies on the straight path between S and L. Therefore, the fundamental relationship is \( D = SF + FL \).

Step 1: Analyzing Statement (I) Statement (I) provides the ratio: \( SF = \frac{3}{5} D \). Substituting this into our fundamental distance equation, we get: \( D = \frac{3}{5} D + FL \) \( FL = D - \frac{3}{5} D \) \( FL = \frac{2}{5} D \). This establishes that \( FL \) is \( 40\% \) of the total distance, but we lack an absolute value for \( D \). Thus, Statement (I) alone is insufficient.

Step 2: Analyzing Statement (II) Statement (II) provides the absolute distance: \( FL = 12 \) km. Without knowing the relationship between segment \( FL \) and the total distance \( D \), we cannot calculate \( D \). Thus, Statement (II) alone is insufficient.

Step 3: Combining the statements From Statement (I), we know \( FL = \frac{2}{5} D \). From Statement (II), we know \( FL = 12 \) km. We set these equal to each other: \( \frac{2}{5} D = 12 \) \( 2D = 60 \) \( D = 30 \) km. Since combining the information allows us to solve for \( D \), the statements are sufficient. {30 km}