GATE CS 2015 Set 1 Q.4 (GA Q.4): Analytical and Logical Reasoning

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

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

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

Both statements together are sufficient, but neither statement alone is sufficient.

Statement I and II together are not sufficient.

Official answer and solution

Official answer: A
From: Official GATE 2015 answer key

Solution

Determine the necessary geometric dimension to find the number of stair steps across vertical floor separation.

The vertical distance between the two floors is $9\text{ feet}$ .

To find the number of steps required, we need the vertical height (riser height) of each step.
Statement I: Each step is $3/4\text{ foot}$ high (riser height). $\text{Number of steps} = \frac{9\text{ feet}}{3/4\text{ foot/step}} = 9 \times \frac{4}{3} = 12\text{ steps}.$ Statement I alone is sufficient.
Statement II: Each step is $1\text{ foot}$ wide (tread depth). This determines the horizontal run of the staircase, not its vertical height or total step count.
Statement II alone is not sufficient.

Hence, Statement I alone is sufficient, but Statement II alone is not sufficient (option A).

Final answer

Common trap

Thinking both riser height and tread depth are needed together to determine the step count.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 1
Question: 4 of 65, printed as GA Q.4
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source