GATE CS 2015 Set 1 QGA-4 — General Aptitude

To find the number of steps in the stairs extending from the first floor to the second floor, we need to relate the total vertical distance between the floors to the dimensions of each step.

• Given: The vertical distance (height) between the two floors is $9$ feet.

Let's evaluate the statements:

1. Statement I: Each step is $3/4$ foot high.
   Knowing the height (rise) of each individual step allows us to calculate the total number of steps required to cover the vertical height of $9$ feet: $$\text{Number of steps} = \frac{\text{Total height}}{\text{Height of each step}} = \frac{9}{3/4} = 12 \text{ steps}$$ Thus, Statement I alone is sufficient to answer the question.


2. Statement II: Each step is $1$ foot wide.
   The width (tread) of each step determines the horizontal run of the staircase, but it provides no information about the vertical height of each step. Without knowing the height of each step, we cannot determine how many steps are needed to span the $9$-foot vertical distance. Thus, Statement II alone is not sufficient.

Therefore, Statement I alone is sufficient, but Statement II alone is not sufficient.