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A stairway is formed by stacking even blocks next to and on top of eac

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Bunuel
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A stairway is formed by stacking even blocks next to and on top of eac [#permalink] New post   16 Aug 2019, 00:56
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A stairway is formed by stacking even blocks next to and on top of each other. If the stairway depicted above is 5 blocks in length and 4 blocks in height, with a thin step at the beginning that does not require a block, and the stairway is only 1 block in width, how many blocks will be required to build such a stairway 20 blocks in length?

A. 80
B. 190
C. 200
D. 240
E. 400

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nick1816
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Re: A stairway is formed by stacking even blocks next to and on top of eac [#permalink] New post   16 Aug 2019, 03:31
Number of blocks required for 5 blocks length staircase= 1+2+3+4= 4*5/2=10

Number of blocks required for 20 blocks length staircase= 1+2+......+18+19= 19*20/2= 190


Bunuel wrote:

A stairway is formed by stacking even blocks next to and on top of each other. If the stairway depicted above is 5 blocks in length and 4 blocks in height, with a thin step at the beginning that does not require a block, and the stairway is only 1 block in width, how many blocks will be required to build such a stairway 20 blocks in length?

A. 80
B. 190
C. 200
D. 240
E. 400

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image1687.jpg
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exc4libur
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A stairway is formed by stacking even blocks next to and on top of eac [#permalink] New post   04 Dec 2019, 06:25
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Bunuel wrote:

A stairway is formed by stacking even blocks next to and on top of each other. If the stairway depicted above is 5 blocks in length and 4 blocks in height, with a thin step at the beginning that does not require a block, and the stairway is only 1 block in width, how many blocks will be required to build such a stairway 20 blocks in length?

A. 80
B. 190
C. 200
D. 240
E. 400


Stairway is made of 5 in length, including 1 thin step, so 4 blocks in length by 4 blocks in height.
If you count the example: 4+3+2+1=10 this is an AP of first natural numbers;
Stairway with 20 in length means 19 blocks in length, or the sum of the first 19 natural numbers:

\(n(n+1)/2=19(20)/2=190\)

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Re: A stairway is formed by stacking even blocks next to and on top of eac [#permalink] New post   04 Dec 2019, 12:39
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Bunuel wrote:

A stairway is formed by stacking even blocks next to and on top of each other. If the stairway depicted above is 5 blocks in length and 4 blocks in height, with a thin step at the beginning that does not require a block, and the stairway is only 1 block in width, how many blocks will be required to build such a stairway 20 blocks in length?

A. 80
B. 190
C. 200
D. 240
E. 400

Show Spoiler
Attachment:
image1687.jpg


To simplify the question, if the length is x then the width is x - 1 and the actual number of blocks needed on the bottom row is x - 1. So for a stairway with 20 blocks in length, the bottom row has 19 blocks. Then we are adding 19 + 18 + ... + 2 + 1. The quick way to do this is to find the median of 1 to 19, the median is equal to the average for a set of consecutive numbers. Then we multiply the median or average by 19 to find the sum since there are 19 numbers. Median = (1 + 19) / 2 = 10. 10 * 19 = 190.

Ans: B
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Re: A stairway is formed by stacking even blocks next to and on top of eac [#permalink] New post   03 May 2021, 17:12
Since we do not need a block for the thin walkway in the beginning, a staircase of length = 20 will require

19 blocks along the bottom length of the staircase

Each consecutive level will require 1 less block, thus the number of blocks will be given by:

19 + 18 + 17 ........ + 2 + 1

Sum of consecutive integers from 1 thru 19 = (1 + 19) * (1/2) * (19)

= (20/2) * 19

= 10 * 19

190 blocks needed

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Re: A stairway is formed by stacking even blocks next to and on top of eac [#permalink]
03 May 2021, 17:12
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