GATE CSE 2015 | Set 1 | GA | Question: 4

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:

1. Each step is $3/4$ foot high.
2. Each step is $1$ foot wide. 

• A. Statements I alone is sufficient, but statement II alone is not sufficient.
• B. Statements II alone is sufficient, but statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Statements I and II together are not sufficient. 

Comments

They mean that the distance between successive floors is 9 feet. Then with statement 1 we can estimate the number of stairs between first and second floors.

---

9/(3/4)=12

Stat 1 alone is sufficient...

Answer 1

• A. Statements I alone is sufficient, but statement II alone is not sufficient.

Comments

plz elaborate ??

---

@priyanka,

Given :  distance between two floors is 9 feet

Solution : 1) each step height is 3/4 feet and since distance between two floors are given we can calculate total no of steps by dividing 9/(3/4).

2) each step width is 1 feet which is not sufficient to find no of steps.

Hence option A is correct.

---

based on statement  $12$ is the result?

---

@Hira Thakur Sir , yes  answer is 12

Answer 2

I think ANSWER is PART (C)

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

Because based on height and width we can calculate effectively how much distance will be traveled in one step.

Each step in general form a right angle triangle in which base is 1 and height is 3/4 so in each step effectively we will travel $\sqrt[2]{1^{2}+(3/4)^{2}}$ 

Please correct me if i am wrong.

Comments

Akhilesh Singla ladder.

---

I think this question is ambiguous.

Considering this question, 2 design of staircase is possible

1)

                _
            _ |
        _ |
    _ |
_ |

2)

Ladder – based staircase.

 

• In 1), both the statement are necessary
• In 2), Only first statement is sufficient.

Be it 1) or 2), in both the cases, we are making assumptions.

NOTE: There can other deigns of staircase too! :) Something like this …

                   _
               _|
            _|
        _|
     _|
__
      |_
         |_
            |_
               |_

---

width of stairs doesn’t matter.

                                                                                                                 ___|

                                                       _____________________________|

             _____________________|

______|

 

                         ____|

                 ____|

         ____|

____|

Answer 3

When we climb from one floor to other, it is the height that matters and not the width of the staircase.Therefore, From statement 1 only, we can figure out that 9 / (3/4) or 12 steps are required.

reference:geeksforgeeks

Answer 4

The number of stairs = Height of the floor / the height of stairs

Hence option A is correct.