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by Nijo » Wed Aug 13, 2014 1:24 am
A contractor combined x tons of a gravel mixture that contained 10% gravel by weight with y tons of a mixture that contained 2% gravel by weight to produce z tons of a mixture that was 5% gravel by weight.
What is the value of x?
1) y = 10
2) z = 16

OA is D

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by GMATGuruNY » Wed Aug 13, 2014 1:43 am
A contractor combined x tons of a gravel mixture that contained 10% gravel G, by weight, with y tons of a mixture that contained 2 percent of the 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
x = 10% gravel
y = 2% gravel.
z = the MIXTURE of x and y = 5% gravel.

To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the percentage for mixture z in the middle.
x 10%-----------5%-----------2% y

Step 2: Calculate the distances between the percentages.
x 10%-----5-----5%----3-----2% y

Step 3: Determine the ratio in the mixture.
The required ratio of x to y is equal to the RECIPROCAL of the distances in red.
x:y = 3:5.

Since x:y = 3:5, and 3+5 = 8, every 8 tons of mixture z is composed of 3 tons of x and 5 tons of y.

Statement 1: y=10
Since x:y = 3:5 = 6:10, x=6.
SUFFICIENT.

Statement 2: z=16
Since x:y = 3:5 = 6:10, and 6+10 = 16, the 16 tons of mixture z must be composed of 6 tons of x and 10 tons of y.
SUFFICIENT.

The correct answer is D.

Check here for a similar problem:
https://www.beatthegmat.com/weighted-ave ... 74015.html
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by [email protected] » Wed Aug 13, 2014 9:41 pm
Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
.1(X) + .02(Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05Z
10X + 2Y = 5Z

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Last edited by [email protected] on Thu Aug 14, 2014 10:19 am, edited 1 time in total.
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by akhilsuhag » Thu Aug 14, 2014 5:44 am
[email protected] wrote:Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
[.1(X) + .02(Y)]/(X + Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05XYZ
10X + 2Y = 5XYZ

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Rich I used two equations as well but our first ones are different. Can you explain why and if I am incorrect

0.1X + .02Y = 0.05 Z

X + Y = Z

You use a little different version of the first equation I used. I mean to say that the amount of gravel in X + amount of gravel in Y is equal to the amount of gravel in Z - as thr is no other source of gravel.

You seem to divide the Left hand side by (X+Y) although.
Please press "thanks" if you think my post has helped you.. Cheers!!
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by GMATGuruNY » Thu Aug 14, 2014 7:04 am
akhilsuhag wrote:
[email protected] wrote:Hi Nijo,

This question is build around an interesting math shortcut: a "system" of equations.

The information in the prompt can be rewritten into 2 equations:

The first equation accounts for the mixture:
[.1(X) + .02(Y)]/(X + Y) = .05(Z)

It can be simplified...

.1X + .02Y = .05XYZ
10X + 2Y = 5XYZ

and

The second equation accounts for the fact that when we mix X tons with Y tons, we get Z tons:
X + Y = Z

Since we're mixing two types of gravel, we don't have to think about using 0 or any negative numbers. The info in the prompt gives us 3 variables and 2 unique equations. If we are given another new equation, then we'll have a "system" of equations, which will allow us to solve for all 3 variables. We're asked for the value of X.

Fact 1: Y = 10

This is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X. We don't actually have to do the math though.
Fact 1 is SUFFICIENT.

Fact 2: Z = 16

This too is a third equation. If we plug this value into the 2 given equations, then we COULD solve for X.
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Rich I used two equations as well but our first ones are different. Can you explain why and if I am incorrect

0.1X + .02Y = 0.05 Z

X + Y = Z

You use a little different version of the first equation I used. I mean to say that the amount of gravel in X + amount of gravel in Y is equal to the amount of gravel in Z - as thr is no other source of gravel.

You seem to divide the Left hand side by (X+Y) although.
Your equation is correct.

I believe that Rich's equation should read as follows:
(0.1X + 0.02Y)/Z = 0.05.
Translated into words:
(gravel in X + gravel in Y)/(Z tons of the mixture of X and Y) = 5 percent.

Simplifying the equation above, we get:
0.1X + 0.02Y = 0.05Z
10X + 2Y = 5Z.

As you can see, your equation and Rich's are the same.
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As a tutor, I don't simply teach you how I would approach problems.
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by [email protected] » Thu Aug 14, 2014 10:18 am
Hi akhilsuhag,

You are absolutely correct; I must have been typing too quickly to notice the mistake. I've gone back and corrected by original post.

GMAT assassins aren't born, they're made,
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by GMATinsight » Fri Aug 15, 2014 11:28 am
Nijo wrote:A contractor combined x tons of a gravel mixture that contained 10% gravel by weight with y tons of a mixture that contained 2% gravel by weight to produce z tons of a mixture that was 5% gravel by weight.
What is the value of x?
1) y = 10
2) z = 16

OA is D

thanks
Solution :

Answer: Option D
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