A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of 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
Please explain.
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gravel mixture
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MartyMurray
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Since you know that x tons had 10% G and y tons had 2% G, you can determine the particular ratio, x:y, necessary for creating a z mixture that contains 5% G.
Also, since you know the ratio of x:y, and since x + y = z, you can determine the ratio x:y:z.
So if you know y or z, you can use the ratios to determine x.
Statement 1: y = 10
From this we can determine x.
Sufficient.
Statement 2: z = 16
From this we can determine x.
Sufficient.
The correct answer is D.
You don't have to do the math to get the answer to this question, but here is a way to calculate the ratio x:y:z.
.1x + .02y = .05(x + y)
.05x = .03y
x:y = 3:5
x + y = z
x:y:z = 3:5:8
Also, since you know the ratio of x:y, and since x + y = z, you can determine the ratio x:y:z.
So if you know y or z, you can use the ratios to determine x.
Statement 1: y = 10
From this we can determine x.
Sufficient.
Statement 2: z = 16
From this we can determine x.
Sufficient.
The correct answer is D.
You don't have to do the math to get the answer to this question, but here is a way to calculate the ratio x:y:z.
.1x + .02y = .05(x + y)
.05x = .03y
x:y = 3:5
x + y = z
x:y:z = 3:5:8
Last edited by MartyMurray on Sat Aug 13, 2016 2:28 pm, edited 1 time in total.
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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
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
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GMATGuruNY
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x = 10% gravelA 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
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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Matt@VeritasPrep
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Here's the general algebraic equation that works pretty much any time you see a problem like this on the GMAT.
(some % of A) + (some % of B) = (some other % of (A + B))
So in our case, this is
10% of x + 2% of y = 5% of (x + y)
and from there it's a cinch
(some % of A) + (some % of B) = (some other % of (A + B))
So in our case, this is
10% of x + 2% of y = 5% of (x + y)
and from there it's a cinch
