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A thin piece of wood of uniform density in the shape of an equilateral

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Bunuel
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A thin piece of wood of uniform density in the shape of an equilateral [#permalink] New post   09 May 2019, 21:20
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64% (01:59) correct 36% (01:56) wrong based on 39 sessions
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A thin piece of wood of uniform density in the shape of an equilateral triangle with side length 3 inches weighs 12 ounces. A second piece of the same type of wood, with the same thickness, also in the shape of an equilateral triangle, has side length of 5 inches. Which of the following is closest to the weight, in ounces, of the second piece?

(A) 14

(B) 16

(C) 20

(D) 33.3

(E) 55.6
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D
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A thin piece of wood of uniform density in the shape of an equilateral [#permalink] New post   11 May 2019, 06:45
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Hello,
Greetings for the day!

To start with, you need to understand that this is not a problem on mensuration. This is, in fact a question which tests you on your proportionality concepts. In particular, direct proportionality is to be applied in this question.

The area of an equilateral triangle is given by the expression (√3/4) * a^2, where a is the length of the side of the equilateral triangle.

The area of the first triangle is therefore (9√3) / 4. The question says that this corresponds to a weight of 12 ounces.

You can observe from two different parts of the question that the thickness of the two pieces of wood is constant. Therefore, we can conclude that the weight of a triangular piece of wood is directly proportional to its area, thickness remaining constant. This means, higher the area, higher the weight, which is corroborated by the fact that all options are bigger than 12.

Now, the area of the second wooden piece will be (25√3)/4. How do we obtain the weight of this piece, knowing the weight of the first piece?

To find out k, which is the weight of the second piece, we need to cross multiply the values since weight is directly proportional to the area. When we do this, we get,
(9√3)/4 * k = (25√3)/4 * 12

On simplification, this gives us k = (100/3) which is equal to 33.3.
So, the correct answer option is D.

In such questions, it’s important that you recognize the hidden clues and use them to your advantage. In this question, the fact that both the triangular wood pieces were of the same thickness is a clue that the weight depends on the area, when thickness is maintained constant. You pick up this clue, you will be on your way to understand that this question intends to test you on proportionality; else you will be left puzzled about why there is no data about the thickness of the pieces.
Also, when two quantities are directly proportional, we write down the corresponding values and CROSS multiply.

Hope that helps!
Arvind,
CrackVerbal Prep Team
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A thin piece of wood of uniform density in the shape of an equilateral [#permalink] New post   11 May 2019, 07:01
ArvindCrackVerbal wrote:
Hello,
Greetings for the day!

To start with, you need to understand that this is not a problem on mensuration. This is, in fact a question which tests you on your proportionality concepts. In particular, direct proportionality is to be applied in this question.

The area of an equilateral triangle is given by the expression (√3/4) * a^2, where a is the length of the side of the equilateral triangle.

The area of the first triangle is therefore (9√3) / 4. The question says that this corresponds to a weight of 12 ounces.

You can observe from two different parts of the question that the thickness of the two pieces of wood is constant. Therefore, we can conclude that the weight of a triangular piece of wood is directly proportional to its area, thickness remaining constant. This means, higher the area, higher the weight, which is corroborated by the fact that all options are bigger than 12.

Now, the area of the second wooden piece will be (25√3)/4. How do we obtain the weight of this piece, knowing the weight of the first piece?

To find out k, which is the weight of the second piece, we need to cross multiply the values since weight is directly proportional to the area. When we do this, we get,
(9√3)/4 * k = (25√3)/4 * 12

On simplification, this gives us k = (100/3) which is equal to 33.3.
So, the correct answer option is D.

In such questions, it’s important that you recognize the hidden clues and use them to your advantage. In this question, the fact that both the triangular wood pieces were of the same thickness is a clue that the weight depends on the area, when thickness is maintained constant. You pick up this clue, you will be on your way to understand that this question intends to test you on proportionality; else you will be left puzzled about why there is no data about the thickness of the pieces.
Also, when two quantities are directly proportional, we write down the corresponding values and CROSS multiply.

Hope that helps!
Arvind,
CrackVerbal Prep Team


Hi ArvindCrackVerbal

Thanks for the great explanation.
But why the weight is not proportion to the only the side of the triangle? why the area? Or is it weight in this case proportional to the volume (density=mass/volume) and the thickness is constant so it is becomes proportional to the area?

Thanks
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CrackverbalGMAT
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Re: A thin piece of wood of uniform density in the shape of an equilateral [#permalink] New post   12 May 2019, 05:25
Mo2men wrote:
ArvindCrackVerbal wrote:
Hello,
Greetings for the day!

To start with, you need to understand that this is not a problem on mensuration. This is, in fact a question which tests you on your proportionality concepts. In particular, direct proportionality is to be applied in this question.

The area of an equilateral triangle is given by the expression (√3/4) * a^2, where a is the length of the side of the equilateral triangle.

The area of the first triangle is therefore (9√3) / 4. The question says that this corresponds to a weight of 12 ounces.

You can observe from two different parts of the question that the thickness of the two pieces of wood is constant. Therefore, we can conclude that the weight of a triangular piece of wood is directly proportional to its area, thickness remaining constant. This means, higher the area, higher the weight, which is corroborated by the fact that all options are bigger than 12.

Now, the area of the second wooden piece will be (25√3)/4. How do we obtain the weight of this piece, knowing the weight of the first piece?

To find out k, which is the weight of the second piece, we need to cross multiply the values since weight is directly proportional to the area. When we do this, we get,
(9√3)/4 * k = (25√3)/4 * 12

On simplification, this gives us k = (100/3) which is equal to 33.3.
So, the correct answer option is D.

In such questions, it’s important that you recognize the hidden clues and use them to your advantage. In this question, the fact that both the triangular wood pieces were of the same thickness is a clue that the weight depends on the area, when thickness is maintained constant. You pick up this clue, you will be on your way to understand that this question intends to test you on proportionality; else you will be left puzzled about why there is no data about the thickness of the pieces.
Also, when two quantities are directly proportional, we write down the corresponding values and CROSS multiply.

Hope that helps!
Arvind,
CrackVerbal Prep Team


Hi ArvindCrackVerbal

Thanks for the great explanation.
But why the weight is not proportion to the only the side of the triangle? why the area? Or is it weight in this case proportional to the volume (density=mass/volume) and the thickness is constant so it is becomes proportional to the area?

Thanks


Hello Mo2men,

GMAT doesn't expect one to remember the technical definition of density in solving this problem. So, that's clearly out of question, isn't it?


"But why the weight is not proportion to the only the side of the triangle?" - In a way, it is actually dependent on the side of the triangle, because the area of the triangle depends on the side, right? If you look closely, the weight is directly proportional to the square of the side of the triangle, thickness being constant.

Hope that clears the air!

Regards,
Arvind,
CrackVerbal Prep Team
GMAT Club Bot
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Re: A thin piece of wood of uniform density in the shape of an equilateral [#permalink]
12 May 2019, 05:25
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