Each step of a staircase is 0.25 meter wide and 0.20 meter high

Question

https://gmatclub.com/forum/download/file.php?id=45217 Each step of a staircase is 0.25 meter wide and 0.20 meter high, as shown in the figure above. All angles shown in the figure are right angles. If the height of the staircase is 3.6 meters and the landing at the top of the staircase is 1 meter wide, how long, in meters, is AB? (A) 3.0 (B) 4.25 (C) 4.5 (D) 5.25 (E) 5.5 Stairs.JPG

u1983 · Accepted Answer

As per the Q the solution might look like : 
total steps = 3.6/0.2 =18
height intervals = 18-1= 17
width covered by 17 intervals = 17*0.25= 4.25m
Hence Ab = 4.25+1=5.25m .....   Ans D

gmat1393 · Answer

Hello HKD1710 I think you for forgot

to attach the image. Thanks!

AdityaHongunti · Answer

We don't necessarily need the image .. just the total height and height of a single stair is enough to know number of steps.

36/2 = 18 stairs

17 stairs have length 0.25
Top stair has 1 m length
So 17* 0.25 + 1 = 5.25

Nice question.

Posted from my mobile device

KanishkM · Answer

So if height = 3.6 m this means that there are in total of 18 such steps, each 0.20 m high

Out of which 2 are consumed as shown in the figure remaining will be 16

We are given length of AB in answer choices, we can subtract 1.25 from it, to get the value which, we have to look out for when

answer options / by 0.25 will give us 16

Only D is the correct choice here.

Shrey9 · Answer

I want to ask
why multiplying 18*0.25 = 4.5 m
option C

wrong here ?
how to make sure that we need to account for 17 steps here and add the last one ?
can anyone clarify on this doubt ?

aliakberza · Answer

Can you please explain why we minus 1 step. Why is the answer not 18 * .25+1= 5.5m?

Thanks

anujpal · Answer

You can also multiply by 18. As total steps are 18, total width will be 18*0.25 = 4.5, but the last step is of 1 m and we have already counted 0.25 out of it, so add 0.75 only to the rest to get total length of AB i.e.. AB=4.5 +0.75 = 5.25.

KUDOS!!

exc4libur · Answer

total height = 3.6m
step height = 0.2m
step width = 0.25m
height of all steps = 3.6/0.2 = 18x
landing = 1m including 1 step
width of all steps = 0.25(18) = 4.5m 
width of all steps + landing = 4.5m - 0.25m + 1m = 5.25m

Answer (D)

Fdambro294 · Answer

Each Vertical Distance Down per Step = .2 m

Total Vertical Distance Down from the Landing Above Point A to the Floor at Point B = 3.6 m

(3.6) / (.2) = 18 Vertical Downward "Lines"

Each of the 18 Vertical "Lines" -----> will have 1 Accompanying Flat, Horizontal Line for the Step so that:

there are 18 Horizontal Steps from Above Point A - to - the Floor at Point B. These 18 Horizontal Steps will measure the Distance AB.

for the 1st Vertical "Line" -------> there is an accompanying Horizontal Landing = 1 m

for the next 17 Vertical "Lines" -----> Each accompanying Horizontal Step = 1/4 m

Distance from AB = (1 meter) + (17) * (1/4 meter) = 1 + 4.25 = 5.25

Answer 
-D-

KarishmaB · Answer

Shrey9

We have total 18 steps with the same height of .20 m. 
The width of each step is 0.25 m but not the last one. The width of the 18th step is 1 m. 
So we account for the width of 17 steps as 17 * .25 and then add 1 m to it to account for the width of the last step.

Answer = 5.25 m

Insane09 · Answer

Solve it waiting 1:30 min
total height is given 3.6m and ht of staircase is 0.20m
3.6/0.2=18m
now 0.20x=18 so x=9
let horizontal distance of staircase be Y=1 and other Horizontal distance be X=0.25
divide 9 in 5+4
5(1)+4(0.25)=5.25

Answer=D

CrackverbalGMAT · Answer

As shown in the figure , the total height is 3.6 m and the height of each staircase is .2 m.
​
So the no of staircase will be 3.6/.2 = 18 staircases.
​
Also we know that the width of each staircase is .25 m and the width of top staircase is 1 m.
So, out 18 staircases, 17 staircases will have a width of .25m each and the top one will have a width of 1 m.
​
Hence, Length AB = 17 * .25 + 1 = 4.25 + 1 = 5.25 m

Thanks,
 Clifin J Francis,
GMAT SME

Anupama_1090 · Answer

The diagram confused me.. It looked like it was broken or something.. Then i realised its not after i read the question. An easy question made tough by the diagram!

KarishmaB · Answer

This is called a scale break and is used to show discontinuity in the diagram. So when you want to show bottom 2 stairs and top 2 stairs but not all others in between, you can use these wavy lines.

Matthewjd24 · Answer

Is this a word problem?

Each step of a staircase is 0.25 meter wide and 0.20 meter high

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Each step of a staircase is 0.25 meter wide and 0.20 meter high

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