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In a stack of boards at a lumber yard, the 20th board counting from th

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In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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New post 17 Jun 2011, 04:09
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In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. how many boards are in the stack?

A) 38

B) 36

C) 35

D) 34

E) 32

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Re: In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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New post 17 Jun 2011, 12:08
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1 2 3 ... 14 15 16 ...................
..............20 19 ................. 1

So the number of boards = 20+14 =34
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Re: In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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New post 04 Jul 2017, 14:44
Baten80 wrote:
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. how many boards are in the stack?

A) 38

B) 36

C) 35

D) 34

E) 32


A board is 20th board counting from the top of the stack . Therefore it will have \(19\) boards above it.

Same board is immediately below the \(16th\) board counting from the bottom of the stack.

Therefore it is on \(15th\) number from bottom of the stack and it will have \(14\) boards below it.

Total number of boards in stack \(= 19 + 14 + 1 = 34\)

Answer (D)...

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In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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New post 05 Jul 2017, 14:42
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Baten80 wrote:
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. how many boards are in the stack?

A) 38

B) 36

C) 35

D) 34

E) 32
Attachment:
stack of boards.jpg
stack of boards.jpg [ 797.06 KiB | Viewed 1048 times ]


After 20 seconds of trying to do the math in my head, I sketched quickly and it got a lot easier.

I've attached a diagram.

Though there are two columns, they represent one stack.

If you were standing in front of this one stack to count boards, for the left column, you would put your finger on the top board and count downward. The right column is the same stack, only this time you have reached down and started counting from the bottom upwards. I slid the two apart to figure out where GREEN and YELLOW fell in relation to boards above and below, and to get arithmetic correct.


Call the board that is 20th counting down from the top GREEN.

That GREEN board sits one below the board that is 16th counting up from the bottom. Call that 16th-from-bottom YELLOW.

GREEN has 19 boards above it. YELLOW has 15 boards below it.

But there is overlap: GREEN takes the ordinal "counting place" of 15th board from bottom (crossed out in diagram to indicate it shouldn't be counted), and

YELLOW takes the ordinal counting place of 19th board from top counting down (also crossed out).

Don't think about the blacked out parts. In ordinal (nth) terms, they don't match, and they'll confuse, which is precisely the point of this question.

So we have 18 + 1 + 1 + 14 = 34.

Answer D

Hope it helps.

Edited to add italicized text.
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Re: In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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New post 14 Jul 2017, 09:42
Baten80 wrote:
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. how many boards are in the stack?

A) 38

B) 36

C) 35

D) 34

E) 32


If the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack, then the 19th board counting from the top of the stack is exactly the 16th board counting from the bottom of the stack. In other words, there are 18 boards above the 16th board counting from the bottom of the stack. Thus, there are 18 + 16 = 34 boards in the stack.

Answer: D
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Re: In a stack of boards at a lumber yard, the 20th board counting from th  [#permalink]

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Re: In a stack of boards at a lumber yard, the 20th board counting from th &nbs [#permalink] 24 Sep 2018, 07:13
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