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A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt

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A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 03 Jan 2016, 12:05
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A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 3/5 of the mixture is water, and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?

A. 4
B. 8
C. 36
D. 60
E. 180

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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 03 Jan 2016, 12:35
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X/3 + 3X/5 + 12 = X.
Solving X = 180.
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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 06 Jan 2016, 11:53
Hi All,

This question can solved in a variety of ways: algebraically, by TESTing THE ANSWERS or with some basic arithmetic and logic. Here's how you can use that last option to avoid a lot of math and still get to the correct answer:

We're told that a mixture is made up of 3 elements:
1) 1/3 of the mixture is sand
2) 3/5 of the mixture is water
3) The remaining 12 pounds of the mixture is gravel.

We're asked for the total weight of the mixture in pounds.

1/3 = .33333
3/5 = .6

So the first two ingredients account for .933333 of the total weight. That's ALMOST ALL of the weight. The final 12 pounds represents such a small overall percentage (.0666666 = 6 2/3%), that the total weight has to be a relatively big number. Looking at the answer choices, there's only one option that makes sense...

Final Answer:

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A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 06 Jan 2016, 18:10
Solving the question using 2 approaches,

1-Testing the answers:

Take choice D= 60
Water content= 60 * 1/3 = 20
Sand content= 60 * 3/5 = 36

Spotting quickly the difference does not have unit digit that equals to 2 in order to make the remaining gravel content equals to 12.

Then answer will be E=180

2- Algebraic approach

spotting the rations, we can detect LCD is 15........> Water content = 5/15 & Sand content= 9/15 then Gravel content = 1/15

X * 1/15 =12 .......NO NEED to multiply as there is only one big number.

Answer is E=180
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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 06 Jan 2016, 20:27
Bunuel wrote:
A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 3/5 of the mixture is water, and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?

A. 4
B. 8
C. 36
D. 60
E. 180


We need to note that we are given the fraction of two elements and the weight of the third.
Therefore, we can find the fraction of the third element in the mixture and equate it to the weight to get a relation in terms of weight.

Fraction of gravel = 1 - 1/3 - 3/5 = 1 - (14/15) = 1/15 = 1/15
Hence 1/3 of the total weight = 12 pounds.

Assume total wight = W
1/15*W = 12
W = 180 (Option E)
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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 06 Jan 2016, 21:42
Hi Mo2men

Your thoroughness (knowing how to approach the prompt in more than one way) is fantastic. For anyone who is reading through this thread, I'd like to add a point to the work that you did when TESTing THE ANSWERS.

With Answer D (60 pounds), the weight of the water would be 20 pounds and the weight of the sand would be 36 pounds. 20+36 = 56 total pounds, which would leave just 4 pounds for the gravel. However, the prompt tells us that there should be 12 pounds of gravel, so Answer D does NOT give us enough pounds. The only way to increase the number of pounds of gravel is if we increase the total weight of the mixture. With these answer choices, there's only one answer that does that - the correct answer.

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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt [#permalink]

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New post 28 Dec 2017, 02:59
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Re: A cement mixture is composed of 3 elements. By weight, 1/3 of the mixt   [#permalink] 28 Dec 2017, 02:59
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