Problem Solving

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

Hi REINE,

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 Answer D: 34 boards...

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

GMAT assassins aren't born, they're made,
Rich

REINE 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. 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