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If the two floors in a certain building are 9 feet apart [#permalink]

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08 Apr 2008, 16:23

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83% (00:26) correct
17% (00:32) wrong based on 194 sessions

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If the 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?

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

The answer is A. There are 12 steps between the floors. The second answer only states how wide the steps are, they could be 1 inch high or 9 feet high, either way we don't know which.

If the two floors in a certain building at 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?

1) Each step is 3/4 foot high 2) Each step is 1 foot wide

Here is my logic

"foot high" so you know something upward the sky, that is, the direction from the first to the second floor. But "foot wide", you can only know the direction toward the ocean.

Think of a really long set of stairs 9 feet high or a really steep set of stairs 9 feet high. The depth of the stairs determines how far horizontally the first stair is from the top stair. The shorter the width of the stairs, the steeper the set of steps. This has nothing to do with the height of each step. The width is the part you step on and the height is the baseboard you see when you are walking up the stairs (also the vertical board).

Re: Relatively simple question (logic & geometry I think) [#permalink]

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18 Feb 2010, 08:16

Ok I can see that even if it zig zags the number of stairs will be the same BUT thats only if we assume that the next stair begins where the previous one ends (height wise)

Edit: the answer explanation states what I expected, that 1 is sufficient because you can get the number of steps by dividing the total height by the height of each step, but again how do I know that we can assume this?

If the 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?

(1) Each step is 3/4 of a foot high (2) Each step is 1 foot wide

because the stairway can be extended in many different ways, e.g. at different slopes, or it can even go up in one direction, and then in the other (sort of zig-zag). Also, each consecutive stair doesn't have to extend by its full height. I guess if you assume that the stairs are placed in one direction, and the next begins where the previous ends (height wise) then A is the answer, but to me it seems that this assumption was not explicated in the question.

The distance given between two floors is in height, not slope or width. so if we consider 1st and 2nd floor it is the height which is 9 ft between both of them. SO how much ever slope we will give to the stairs their height should sum to 9 ft dats y we can conclude from the first point dat no of stairs = 9 ft / 3/4 ft or 12 sets. This is why A is the answer.
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Re: If the two floors in a certain building are 9 feet apart [#permalink]

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20 May 2014, 10:29

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If the 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?

(1) Each step is 3/4 foot high. Since each step is 3/4 foot high and the stairs rises 9 feet from the first floor to the second, the number of steps must be \(\frac{9}{(\frac{3}{4})}=12\). Sufficient.

(2) Each step is 1 foot wide. Clearly insufficient.

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