GATE EE 2015 Set 1 — Question 4
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Question
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.
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.
Correct answer
(A) Statement I alone is sufficient, but statement II alone is not sufficient.
Solution
To find the number of steps, we need to know the total vertical distance between the floors and the height of each step.Given:
Total vertical distance between two floors = 9 feet.Statement (I): Each step is 3/4 foot high.
From this statement, we can calculate the number of steps: Number of steps = steps.
So, Statement I alone is sufficient.Statement (II): Each step is 1 foot wide.
This statement gives information about the width of the step, which is irrelevant to the number of steps required to cover a vertical distance. So, Statement II alone is not sufficient.Therefore, Statement I alone is sufficient, but Statement II alone is not sufficient.The correct option is (A).
Total vertical distance between two floors = 9 feet.Statement (I): Each step is 3/4 foot high.
From this statement, we can calculate the number of steps: Number of steps = steps.
So, Statement I alone is sufficient.Statement (II): Each step is 1 foot wide.
This statement gives information about the width of the step, which is irrelevant to the number of steps required to cover a vertical distance. So, Statement II alone is not sufficient.Therefore, Statement I alone is sufficient, but Statement II alone is not sufficient.The correct option is (A).
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