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by j_shreyans » Mon Nov 03, 2014 11:46 am
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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by GMATGuruNY » Mon Nov 03, 2014 11:50 am
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
1
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19 = 16
20 = 15
14
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2
1

In the rendering above:
The red values represent the number of boards when counting from the TOP.
The blue values represent the number of boards when counting from the BOTTOM.
The two middle rows with big numbers satisfy the constraint that RED BOARD 20 is directly below BLUE BOARD 16.

Total number of boards = (red boards 1-18) + (2 middle rows with big numbers) + (blue boards 1-14) = 18+2+14 = 34.

The correct answer is D.
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by Brent@GMATPrepNow » Mon Nov 03, 2014 11:56 am
j_shreyans 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

OAD
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

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by [email protected] » Mon Nov 03, 2014 5:28 pm
Hi j_shreyans,

As Mitch and Brent have shown, how you approach this question comes down to how you "see" the work.... and then you do the work.

This prompt is perfect for TESTing THE ANSWERS.

We're told that the 20th board from the top is immediately BELOW the 16th board from the bottom. This means that some of the boards have been counted TWICE, so the total MUST be less than 36.

Let's TEST 34...

With 34 boards....

1 to 19, 20th, 21 to 34 --> this accounts for the 20th board from the top

34 to 20 = 15 boards

34 to 20, 19th, 18 to 1 --> this accounts for the 16th board from the bottom

In this scenario, the 20th board from the top is immediately below the 16th board from the bottom, so 34 IS the total number of boards.

Final Answer: D

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by Mathsbuddy » Wed Nov 05, 2014 5:38 am
{From the top, the 19th board} = {from the bottom, the 16th board}
Therefore this board has 18 boards above and 15 boards below
Total boards = 18 + 1 (this board) + 15 = 34
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by Brent@GMATPrepNow » Sat Jan 13, 2018 9:11 am
j_shreyans 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

OAD
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,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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