Based on the given statements, select the most appropriate option to solve the…
2015
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 1 alone is sufficient, but statement 2 alone is not sufficient.
- B.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient.
- C.
Both statement together are sufficient, but neither statement alone is sufficient.
- D.
Statement 1 and 2 together are not sufficient.
Attempted by 8 students.
Show answer & explanation
Correct answer: A
Answer: The information that each step is 3/4 foot high is sufficient; the information that each step is 1 foot wide is not.
Calculation:
Vertical distance between floors = 9 feet.
Height of each step = 3/4 foot.
Number of steps = 9 ÷ (3/4) = 9 × 4/3 = 12 steps.
Why the step width is not sufficient:
A step’s width (1 foot) tells the horizontal run of the stair, not the vertical rise per step. Without the vertical rise per step, you cannot compute how many steps are needed to span a given vertical distance.
Conclusion: The height of each step (3/4 foot) alone determines the number of steps (12), so the height statement alone is sufficient; the width statement alone is not.