Question

Two friends rented a truck from a store. The store charges \$19.99 per hour or portion thereof for rent and \$0.55 per mile travelled, with no charges for fuel. How much did they pay the store? Statement (I): Total round trip was 100 miles.
Statement (II): They returned the truck after 3 hours 20 minutes.

• 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:

When a cost depends on two independent variables (time and distance), both must be provided or solvable.

Answer 1

The Correct Option is C

Concept: The total payment is calculated using the cost structure: Total Cost = (Hourly Rate \(\times\) Total Hours) + (Mileage Rate \(\times\) Total Miles).

Step 1: Analyzing Statement (I) This statement tells us the total mileage = 100 miles. Using the mileage rate (\$0.55/mile), we can calculate the mileage cost: MATH_3b6e98e9c11144f39222a62f75946885. \par However, the rental duration (time) is unknown, so the rental cost cannot be calculated. \par Thus, Statement (I) alone is insufficient. \bigskip Step 2: {\color{red}Analyzing Statement (II)} \par This statement tells us the duration = 3 hours 20 minutes. \par Using the hourly rate (\$19.99/hr), we can calculate the rental cost. However, the total mileage is unknown, so the mileage cost cannot be calculated. Thus, Statement (II) alone is insufficient.

Step 3: Combining the statements We convert the duration to hours: 3 hours 20 minutes = \( 3 + \frac{20}{60} = 3.333 \) hours. Rental Cost = \( 19.99 \times 3.333 = \$66.63 \) (approx). Mileage Cost = \( 100 \times 0.55 = \$55.00 \). Summing these gives the total payment. Since both components are now known, the statements are sufficient. {Total Cost is calculable}