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

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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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

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

We can actually quickly try it out with lesser number of planks.

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

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

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

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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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 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:

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

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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Hi, i'm just curious. What if the question is changed to:
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately above the 16th board counting from the bottom of the stack. How many boards are in the stack?

How do we resolve it? I have some problem in imagining these kind of things..

Hi tagheueraquaracer,

The reason why some people find this prompt a little confusing is because some of boards are in BOTH 'groups' (the group that starts at the top AND the group that starts from the bottom) - and you have to account for that 'overlap' to correctly answer the question. In these sorts of story-problems, it can sometimes help to draw a picture so that you can 'see' what is being described (so you don't have to "imagine" what you are reading about). Here's how you could do that with the original prompt:

1) Start by drawing a vertical line and labeling it '20 boards' and put a mark at the BOTTOM of the line with the label "20th board."
2) Near the bottom of your first line - and slightly to the right - draw another vertical line going further 'down' and label it '16 boards.' put a mark at the TOP of this line with the label "16th board"
3) Based on the description in the prompt, we're told that the 16th board from the bottom is 'one above' the 20th board from the top... meaning that the 16th from the bottom is ALSO the 19th from the top. Add that additional description to your drawing.

Now, looking at your drawing, you should notice that the 19th and 20th boards from the top are ALSO the 16th and 15th boards from the bottom. Those 2 boards appear in BOTH groups. To find the total number of boards, we need to take those 2 boards and add in all of the other boards that are only in one of the groups (that would be the 20 - 2 = 18 other boards from the top AND the 16 - 2 = 14 other boards from the bottom).

2 + 18 + 14 = 34

If you were to change the question in the way that you describe, then there would be NO overlap - and you would just be adding 20 and 16. While you will see some easy questions on the GMAT (regardless of how well you are performing), you probably won't see a story-problem that would be that easy.

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

Simply test the principle with smaller numbers (and create a visual if necessary).

If the 6th board counting from the TOP of the stack is located BELOW the 2nd board counting from the BOTTOM of the stack, for example, then this simply means there are 6 total boards in the stack.

6 + 2 = 8, yet there are only 6 boards in the stack. This tells us that we can simply add the two numbers together, and then subtract 2 to account for the overlap. 20 + 16 - 2 = 34.

Another way to think about it: If the 3rd person in line counting from the FRONT is BEHIND the 2nd person in line counting from the BACK, then there are actually only 3 + 2 = 5 - (2 overlap) = 3 people in line.

what category does this question fall under? ie what topic is it?

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