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

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Intern
Joined: 12 Nov 2007
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In a stack of boards at a lumber yard, the 20th board [#permalink]

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12 Nov 2007, 20:45
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

I can find the answer easily enough by writing down all the numbers and back solving using the answers, but there has to be an easier way to attack this problem. Any ideas?
Manager
Joined: 25 Jul 2007
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12 Nov 2007, 20:57
There is no need to backsolve.

We will call our board B. It says that the board is 20th from the top of the stack.
i.e:

19
B
..
...

It also says that this board B is one below the 16th board from the bottom. i.e. it is the 15th board from the bottom.

19
B
14

19+B+14=34 boards in the stack.

Hope this helps.
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Joined: 09 Aug 2006
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12 Nov 2007, 21:26
showtime12 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

I can find the answer easily enough by writing down all the numbers and back solving using the answers, but there has to be an easier way to attack this problem. Any ideas?

From the top, the board after the 19th board, i.e., the 20th board from the top is the 15th board from the bottom. Total boards = 19 + 15 = 34.
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13 Nov 2007, 12:38
That makes sense. Thanks

showtime12 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

I can find the answer easily enough by writing down all the numbers and back solving using the answers, but there has to be an easier way to attack this problem. Any ideas?
Re: Counting Problems   [#permalink] 13 Nov 2007, 12:38
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