A church C is on a hilltop at a height 300 feet from the ground and is

Question

A church C is on a hilltop at a height 300 feet from the ground and is reached only through stairs of steps of width 1/3 foot. How many steps must be climbed to reach the entrance of church C from the bottom A of the stairs?

(1) The height of each step is 1/2 foot.
(2) Church C is located at a horizontal distance of 300 feet from the bottom of the stairs A.

Azedenkae · Answer

I am a bit confused by this question.

Statement (1): Knowing the height of each step here means you don't need to factor in the width of each step. Given the vertical height of the church from the ground (300ft) and the height of each step (1/2ft), you can easily calculate that the number of steps must be 300/(1/2) = 600 steps. So statement (1) is sufficient.

Statement (2): Knowing the horizontal distance here means you don't need to factor in the vertical height of the church. Given the width of each step (1/3ft) and the horizontal distance (300ft), you can easily calculate that the number of steps must be 300/(1/3) = 900 steps. So statement (2) is sufficient.

Each statement alone is sufficient means that the answer is D. However... when I calculate it as above, the answers are actually different (600 steps for (1) vs. 900 steps for (2)). So... I must have approached this incorrectly I think? I didn't think the statements can contradict each other.

baru · Answer

Given : height 300 feet from the ground
=> As it forms a Right Triangle , we need length of hypotenuse and step height or total number of steps

(1) The height of each step is 1/2 foot.=>No hypotenuse given=> Insufficient 
 
(2) Church C is located at a horizontal distance of 300 feet from the bottom of the stairs A. 
 we can find hypotenuse with Pythagorean theorem, but need step height ==> Insufficient

Combining 1 & 2 we get hyp & step height ==> Sufficient

Option C

blueviper · Answer

Total height = 300 ft

Step width = 1/3 ft

1) Total Steps = Total Height/height of single step = 300/1/2 = 600 steps. Sufficient!

2) Total Steps = Total Horizontal distance/width of single step = 300/1/3 = 900 steps. Sufficient!

Answer is 'D'

Jerry1982 · Answer

Ans C

to answer the question we first need to find diagonal length of each step and then length of hypotenuse of right triangle formed by a point on ground, church on hill top and stairs step .

S1 gives h = 1/2 ft w= 1/3 ft but l= ??, so we cannot find diagonal length of a stair. also we do not know length of hypotenuse.

S2 : First , from question stem we already know that vertical distance between point B on ground and Church C = 300 ft. S2 provides us further information that horizontal distance between point A and C (Point A is where the first stair will be laid) is 300 ft , hence we can deduce that BC = 300 as well.
Now we know the base and height f triangle , using Pythagoras theorem we can calculate Hypotenuse. 
But we do not know Height of stairs hence S2 is also ISF.

Combine 1 & 2 , From s1 we get stairs height = 1/2 and from S2 we get Hypotenuse . hence SF

amanvermagmat · Answer

Hello

In GMAT,  whenever the answer is D, both statements should give the same answer . Here in this case we are getting '600 steps' from first statement and '900 steps' from second statement (different answers), so probably we need to re-look at our analysis.

krish76 · Answer

answer (A) in my opinion.

statement 1 - We know the height we have to climb and we know the height of individual stairs.. width should be irrelevant, even if it is not it is additional information and doesnt harm. SUFFICIENT

statement 2 - we know the base and height of triangle and can figure out hyp. now, can we have 2 or more different total steps to climb when we know the slanting distance we need to cover? if i assume all individual steps are of same height then no we cant have. but what if individual step heights are different?

I would probably have chosen A or D in test.

jackspire · Answer

Hello  Jerry1982  &  baru ,

Here the question is asking for the total number of steps we need to take, but not asking for the total distance we need to cover.
If we were asked about the distance someone has to cover to reach the church, then we would have needed the hypotenuse or length of each step.

From statement-1 we can calculate the number of steps = total height/height of each step.
From statement-2 we can calculate the number of steps = total horizontal length/width of each step.

So, the answer is D.
Hope it helps.

I wrongly chose the option A because I couldn't correlate the horizontal length of the church and width of each step.
My mistake.

baru · Answer

We usually donot builds steps vertically , So --> total Vertical height/height of each step -Is wrong
   It should be Hupotenues height to calculate the total number of steps , Hence C

bumpbot · Answer

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A church C is on a hilltop at a height 300 feet from the ground and is

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