Staircase Step Calculation: Data Sufficiency Analysis

The question asks us to find the total number of steps required for a staircase that connects two floors, which are separated by a vertical distance of 9 feet.

Analyzing Statement I

Statement I tells us that "Each step is 3/4 foot high."

To find the total number of steps, we need to divide the total vertical distance between the floors by the height of each individual step.

• Total vertical distance = 9 feet.
• Height of each step = $\frac{3}{4}$ foot.

The calculation for the number of steps is as follows:

Number of steps = \(\frac{\text{Total vertical distance}}{\text{Height per step}}\)

Number of steps = \(\frac{9 \text{ feet}}{\frac{3}{4} \text{ feet/step}}\)

Number of steps = \(9 \times \frac{4}{3}\) steps

Number of steps = \(3 \times 4\) steps

Number of steps = 12 steps.

Since we can calculate a specific number of steps (12) using only Statement I, Statement I alone is sufficient to answer the question.

Analyzing Statement II

Statement II states that "Each step is 1 foot wide."

The width of a step relates to the horizontal length or depth of the staircase, not its vertical rise. The number of steps is determined by the total vertical distance and the height of each step.

Knowing the width of each step does not help us determine how many steps are needed to cover the 9-foot vertical distance between floors.

Therefore, Statement II alone is not sufficient to answer the question.

Conclusion on Sufficiency

Based on the analysis:

• Statement I alone is sufficient.
• Statement II alone is not sufficient.

This situation corresponds to the option where Statement I alone is sufficient, but Statement II alone is not.