Based on the given statements, select the most appropriate option to solve the given question. If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building? Statements: I. Each step is 3/4 foot high. II. Each step is 1 foot wide. A. Statement I alone is sufficient, but statement II alone is not sufficient. B. Statement II alone is sufficient, but statement I alone is not sufficient. C. Both statements I and II together are sufficient, but neither statement alone is sufficient. D. Both statements I and II together are not sufficient.

GATE 2015 · General Aptitude · Statement Sufficiency · medium

Answer: Option A — Statement I alone is sufficient. With each step 3/4 foot high and a 9-foot floor separation, the number of steps = 9 / (3/4) = 12 steps. Statement II (step width = 1 foot) is irrelevant to counting steps for a given vertical rise.

1. Identify what is needed to count steps: The two floors are 9 feet apart (total vertical rise = 9 ft). To find the number of steps, we need to know how much vertical height each step covers. This is the riser height, not the tread width.
2. Test Statement I alone: Statement I says each step is 3/4 foot high. Using the formula: steps = 9 / (3/4) = 12. This is a unique, definite answer. Statement I alone IS sufficient.
3. Test Statement II alone: Statement II says each step is 1 foot wide. Step width is a horizontal measurement. Knowing the width does not tell us how high each step is, so we cannot compute how many steps cover 9 feet of vertical rise. Statement II alone is NOT sufficient.
4. Determine the correct option: Statement I alone is sufficient (gives 12 steps). Statement II alone is not sufficient (gives no information about vertical coverage). This matches option A.