A pagoda “P” is situated on an apex of a hill at a height of

Question

A pagoda “P” is situated on an apex of a hill at a height of 200 feet from the ground and is reached only through stairs of steps of width 1⁄2 foot. How many steps must be climbed to reach the entrance of the Pagoda “P” from the bottom “B” of the stairs?

(1) The height of each step is 1/3 foot.
(2) Pagoda P is located at a horizontal distance of 200 feet from the bottom of the stairs B.

Solution: 
Statement (1) says, height of each step is 1/3 foot.
Let there are a total of “m” steps from bottom B to entrance of P.
So the equation is simple now, m × 1/3 = 200
 Or, m = 600 .
Statement (1) is sufficient to evaluate the answer alone.

Now statement (2), the horizontal distance is 200 feet; it means now you have to think the pagoda at a bottom surface and it is now at a horizontal distance of 200 feet from the first stair B.

When you think some vertical structure as horizontal, then the width of steps or anything else becomes the part of the horizontal distance not the height anymore.

So let the number of steps again “m” and width is 1⁄2 foot here now.
.
Now the equation becomes simple again, m × 1/2 = 200
 Or, m = 400 .
Statement (2) is also sufficient to evaluate the answer alone.

Thus the answer is (D)

crash · Answer

IMO D

Both are independently sufficient. As always made sure the wording is such that there is no loophole, ambiguity that might lead to either a or b not being sufficient.

kumar23badgujar · Answer

Hi,

I am getting a bit confused. Doesn't second statement mean that the pagoda is at an height of 200 feet and at a horizontal distance of 200 feet (imagine a isosceles Pythagoras triangle)?

Correct me if I am wrong. Because according to this logic, the answer should then be only A.

Thx

crash · Answer

Yes it does. However, we need to know either the width of the step or the height to answer correctly.

Imagine the below stairway to heaven.
 
  ______  _|
  _____  _|
  ___  _|
 _ _|

In above example, you need either the width of the _ of the height of the |. And you can figure out number of steps.

Asifpirlo · Answer

i uploaded a picture for you to make it clear. watch it

amitbharadwaj7 · Answer

I am not convinced with the solution. In my view
a) Statement -1: it informs the height of each step i.e. 1/3 feet, but the insufficiency is how much horizontal distance to be be cover. The information given in the question of 1/2 ft width of the step is not utilized and it is ilogical to avoid the width of the step. For example if the horizontal distance of starting step varies, we may cover the vertical distance but may not be the horizontal distance.

b) Statement 2:- It informs the horizontal distance which is to be covered, but what about the height of stairs, if the height of stairs is too less, we may cover the horizontal distance but not the vertical distance. the objective is to reach the pagoda enterance. Again in this statement the height of mountain or location of pagoda at 200 ft is ignored, which sounds ilogical.

In case answer is D, the number of steps arrived from both the statement 1 and 2 should match, which is again not happening.

According to me, answer should be E. Please correct me if I am wrong.

Asifpirlo · Answer

have you seen the diagram?
see it well you will have it.
however brother, two things to say,
1. when we rise higher we just count the height not width.
2. when we walk on the road(horizontal) we count width not height.

watch the diagram from down to up
and then left to right........ you will have it brother.....

stne · Answer

It also does seem that the answer should be E or C and not D , however I could be wrong ,

a) statement a Gives 600 steps , however this contradicts with statement 2 
statement 2 says pagoda is 200 feet in horizontal distance so if there are 600 steps and each step is 1/2 feet wide then we travel 300 feet and overshoot the pagoda

b) In the same way if we have 400 steps according to B and each step is 1/3 feet in height then total height we would reach is approx 133 feet , so we would be short of pagoda.

if we consider an isosceles right triangle with base 200 and height 200 then Hypotenuse is  200 \sqrt{2}

how do we get the correct the number of steps

Can some one help me with this , thank you

Paris75 · Answer

For me the Answer should be E.

First, the author neglects either the hight or the width of the location.

Second, the conclusion he gave lead to two different answers m=400 and m=600. One question, two answers?

For A: we know how much steps we need to get to a certain point. But where is that point?

For B: Horizental means a basis. I am at 40 meter in horizontal distance from Obama but at 100 meters hight.

Therefore, even A and B do not give enought information.

HIH.

jlgdr · Answer

Think vertically, then think horizontally, that is flip it around. Statement 2 tells you that the the Pagoda is 200 feet from the stairs, therefore now the width of 1/2 foot becomes the height. Therefore, we know how many stairs we need in order to reach a level of 200 feet.

Hope this clarifies
Cheers
J

Hope this clarifies
Cheers
J

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A pagoda “P” is situated on an apex of a hill at a height of

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