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# A contractor combined x tons of a gravel mixture that contai

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Director
Joined: 24 Oct 2005
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A contractor combined x tons of a gravel mixture that contai [#permalink]

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09 Apr 2006, 16:49
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A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x ?

(1) y = 10
(2) z = 16

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contractor-combined-x-tons-of-a-gravel-mixture-that-102681.html
[Reveal] Spoiler: OA

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09 Apr 2006, 16:57
C

g(x) = 10/100 * x
g(y) = 2/100 * y

g(x) + g(y) = g(z) = 5/100 * z

10x + 2y = 5z

so u need both z and y to find the value of x!

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09 Apr 2006, 21:42
Considering both the cases, we get the following equations:

Gravel: 10x/100 + 2y/100 = 5z/100
Non-Gravel: 90x/100 + 98y/100 = 95z/100

Case A: y = 10
=====

10x + 20 = 5z
90x + 98y = 95z

Substituting y = 10, we can solve for x = 6

Case B: z = 16
=====

10x + 2y = 80
90x + 98y = 1520

Substituting z = 16, we can solve for x = 6.

So, (A) and (B) are independently sufficient to answer the query.

So the answer is D.
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10 Apr 2006, 19:21
It is quite simple. Match weights of gravel and non-gravel.

Gravel --> 10% of x + 2% of y = 5% of z
Therefore everything that remains must be non-gravel or whatever constituent is used in the mixture.

So,

Non-Gravel -->

90% of x (this is what remains from the first mixture) +
98% of y (this is what remains from the second mixture) =
95% of z (this is what remains from the third mixture)

So you get the equation that you have in bold.
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10 Apr 2006, 20:14

n1/n2 = (c2-cm)/(cm-c1)

c1, c2 and cm are concentrations , all given

n1 = x
n2 = y = statement A

statement b gives Z , which indirectly gives y in terms of x

So D

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13 Apr 2006, 01:00
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D is my choice

Question gives us x+y=z and also .10x+.02y=.05z = .05(x+y)

1) gives y=10
so we can solve .10x+.02y=.05(x+y)
so sufficient

2) x+y=16 so .10x+.02y=8 ... two unique equation can solve it
so sufficient

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14 Apr 2006, 10:33
Here is what i think
if you take total X + Y = Z (over all mass balance)
and 0.1X + 0.02 Y = 0.05 Z (Gravel balance)
We have 3 variable and two equations. But if you know the value of Z as in the second case, you can find out X and Y.
So I think Z = 16 should be sufficient to solve the equations.
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Director
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16 Apr 2006, 12:35
I learnt a nice way of solving mixtures today and learnt that best to rewrite the problem..

So question is: x/10 + y/50 = 5/100(x+y)
z = x+y given.

1. y = 10, subs y, you get x. Suff.. So now down to A or D.
2. z = 16, so y = 16-x, subs in the question, you get X. so suff.

Hence D...

Hopefully this helps to a lot of us.. Under time pressure to get this right is whole another thing!

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28 Aug 2013, 04:42
Zooroopa wrote:
Considering both the cases, we get the following equations:

Gravel: 10x/100 + 2y/100 = 5z/100
Non-Gravel: 90x/100 + 98y/100 = 95z/100

Case A: y = 10
=====

10x + 20 = 5z
90x + 98y = 95z

Substituting y = 10, we can solve for x = 6

Case B: z = 16
=====

10x + 2y = 80
90x + 98y = 1520

Substituting z = 16, we can solve for x = 6.

So, (A) and (B) are independently sufficient to answer the query.

So the answer is D.

Ohhh this is crazy...
that means you need to guess, that there is also non gravel equation suppose to be.

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Re: A contractor combined x tons of a gravel mixture that contai [#permalink]

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28 Aug 2013, 09:39
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A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x ?

Set the equation: $$0.1x+0.02y=0.05(x+y)$$, where $$x+y=z$$ --> $$5x=3y$$ --> Q: $$x=?$$

(1) $$y=10$$ --> $$5x=3y=30$$ --> $$x=6$$. Sufficient.

(2) $$z=x+y=16$$ --> $$y=16-x$$ --> $$5x=3y=3(16-x)$$ --> $$x=6$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-contractor-combined-x-tons-of-a-gravel-mixture-that-102681.html
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Re: A contractor combined x tons of a gravel mixture that contai   [#permalink] 28 Aug 2013, 09:39
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# A contractor combined x tons of a gravel mixture that contai

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