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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 Updated on: 23 Jul 2019, 01:35
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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

Originally posted by netcaesar on 14 Nov 2006, 13:59.
Last edited by Bunuel on 23 Jul 2019, 01:35, edited 3 times in total.
Renamed the topic and edited the question.
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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 03 Sep 2012, 05:18
17
15
vidhya16 wrote:
Guys,

Im confused with the phrase "immediately below 16 from the bottom". When you count something and you say immediately below something doesnt that it mean next number in the counting. In this example it will be 17th. How do you guys say it is 15th from the bottom?

Any clarification will help on Tuesday attempt.

Thanks


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

There are some number of boards stacked.

20th board from the top is immediately below the 16th board from the bottom:

1
2
3
.
.
.
16
20 15
14
13
.
.
.
3
2
1


As you can see 20th board from the top is immediately below the 16th board from the bottom. The total number of boards 20(red)+14(blue)=34.

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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New post 14 Nov 2006, 14:32
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3
20th board from top is 15th (immediately below the 16th board) from bottom. Therefore, there are 14 more boards below the 20th board (from top).
Total number of boards = 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 02 Sep 2012, 08:17
Guys,

Im confused with the phrase "immediately below 16 from the bottom". When you count something and you say immediately below something doesnt that it mean next number in the counting. In this example it will be 17th. How do you guys say it is 15th from the bottom?

Any clarification will help on Tuesday attempt.

Thanks
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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 19 Feb 2015, 09:02
2
1
We can actually quickly try it out with lesser number of planks.

Say 4th from the top is immediately below 3rd from the bottom.

-------------
-------------
-------------
-------------
-------------

Total number of planks = 4+3-2 = 5

This in fact would be the case with any plank. For example, 3rd from the top is below 4th from the bottom.

Total number of planks = 3+4-2 = 5

Here, 20th from the top is below 16th from the bottom
-> Total number of planks = 20+16-2 = 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 18 Oct 2015, 12:18
novice12 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

Please support your answer with explanation.


We need the 20th board, when we start counting from the top.
This board is immediately below the 16th board from the bottom. i.e. This is the 15th board from the bottom
Hence we have 14 more boards below this.

Total number of boards = 14(No. of boards below the one in consideration) + 20(No. of boards above the one in consideration) = 34 Option 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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New post 05 Jul 2017, 15:42
2
1
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 9667 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 13 Jan 2018, 10:09
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netcaesar 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


Let's start from the bottom and work our way up:

We'll start with the 16th board counting from the bottom of the stack

Right BELOW that 16th board, we have a board that we'll call Larry.
So, Larry is the 15th board counting from the bottom of the stack.
So, starting from the bottom and working our way up to Larry, we have 15 boards so far.

Larry is the 20th board counting from the TOP of the stack
In other words, there are 19 boards ABOVE Larry.
So, including those 19 boards, we now have 34 boards in TOTAL.

Answer: D

Cheers,
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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 15 Mar 2018, 13:30
Hi All,

Since the answers to the question are all numbers, we can use the answers 'against' the prompt and TEST THE ANSWERS. Here's how…

Let's start with Answer B.

Answer B: 36 boards

IF the number of boards was 36, then the 20th board from the top would be the 17th board from bottom, which would be UNDER the 18th board from the bottom. This is NOT a match for what we were told. Elimate B. Now we know that the number of boards has to be SMALLER. Let's test D next.

Answer B: 34 boards

IF the number of boards was 34, then the 20th board from the top would be the 15th board from the bottom, which would be UNDER the 16th board from the bottom. This IS a match for what we were told, so this MUST be the answer.

Final Answer:

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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 30 Mar 2018, 10:59
2
netcaesar 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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New post 07 Oct 2018, 22:40
vidhya16 wrote:
Guys,

Im confused with the phrase "immediately below 16 from the bottom". When you count something and you say immediately below something doesnt that it mean next number in the counting. In this example it will be 17th. How do you guys say it is 15th from the bottom?

Any clarification will help on Tuesday attempt.

Thanks

vidhya16,

Hey If this pictorial representation helps you.

Attachment:
IMG_2762.jpg
IMG_2762.jpg [ 1.35 MiB | Viewed 20187 times ]
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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 Dec 2018, 10:40
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E68D1F8A-38CD-40E5-9716-A83F53D26438.jpeg [ 512.63 KiB | Viewed 17615 times ]

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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 07 Jul 2019, 07:53
We can actually quickly try it out with a lesser number of planks.

Say 4th from the top is immediately below 3rd from the bottom.

-------------
-------------
-------------
-------------
-------------

Total number of planks = 4+3-2 = 5

This, in fact, would be the case with any plank. For example, 3rd from the top is below 4th from the bottom.

Total number of planks = 3+4-2 = 5

Here, 20th from the top is below 16th from the bottom
-> Total number of planks = 20+16-2 = 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 07 Jul 2019, 08:29
How many boards can be translated to: # of boards above 20th board + 20th board + # of boards below 20th board

# of boards above 20: 19

20th board: 1

# of boards below 20: Since it is below 16th board from the bottom of the stack, the 20th (from the top) would be the 15th from the bottom, so it has 14 boards below:14

1+14+19 = 34, (D) is the answer.
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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   [#permalink] 23 Jul 2019, 01:31
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