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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gmat_chanakya
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GMATGuruNY
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1gmat_chanakya 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
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19 = 16
20 = 15
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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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Hello,
As per the problem we can track that boards are double counted 2 times. The 20th board was counted in the set "16 from the bottom", and the 16th board was counted in the set "20 from the top". So, (20-1) + (16-1) = 34.
OR
From top, the board after the 19th board, is the 20th board from the top is the 15th board from the bottom. Total boards = 19 + 15 = 34.
Regards,
Tushar
As per the problem we can track that boards are double counted 2 times. The 20th board was counted in the set "16 from the bottom", and the 16th board was counted in the set "20 from the top". So, (20-1) + (16-1) = 34.
OR
From top, the board after the 19th board, is the 20th board from the top is the 15th board from the bottom. Total boards = 19 + 15 = 34.
Regards,
Tushar
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theCodeToGMAT
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-- 20th from TOp & 15th from Bottom
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19 above the 20th BOARD
14 below the 20th BOARD
So, Total Board= 19 + 1 + 14 = 34
[spoiler]{D}[/spoiler]
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-- 20th from TOp & 15th from Bottom
.
.
19 above the 20th BOARD
14 below the 20th BOARD
So, Total Board= 19 + 1 + 14 = 34
[spoiler]{D}[/spoiler]
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Hi gmat_chanakya,
The answers to the question are all numbers; in this scenario, we can TEST THE ANSWERS. Here's how...
Let's start with answer B. If the number of boards was 36, 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. If the number of boards was 34, 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: D
GMAT assassins aren't born, they're made,
Rich
The answers to the question are all numbers; in this scenario, we can TEST THE ANSWERS. Here's how...
Let's start with answer B. If the number of boards was 36, 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. If the number of boards was 34, 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: D
GMAT assassins aren't born, they're made,
Rich
