Source: GMAT Prep
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.
The OA is D.
One equation will be 10x + 2y = 5z.
Other equation, x + y = z.
Statement 1: y = 10. Sufficient 3 equations and 3 variables.
Statement 2: z = 16. Sufficient 3 equations and 3 variables.
Hence, D is the correct answer.
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A contractor combined x tons of a gravel mixture that
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Let's use some weighted averages to solve this questionAAPL wrote:Source: GMAT Prep
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.
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Target question: What is the value of x ?
Given: 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.
First, we can write: x + y = z
Also, the total weight of the mixture = z (aka x + y)
So, when we apply the above formula, we get: 5% = (x/z)(10%) + (y/z)(2%)
Ignore the % symbols: 5 = (x/z)(10) + (y/z)(2)
Multiply both sides by z to get: 5z = 10x + 2y
Since x + y = z, we can rewrite the above equation as: 5(x +y) = 10x + 2y
Expand: 5x + 5y = 10x + 2y
Simplify to get: 5x - 3y = 0
Now onto the statements!!!!!
Statement 1: y = 10
Replace y with 10 to get: 5x - 3(10) = 0
Solve to get, x = 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 16
In other words, x + y = 16
So, we have:
5x - 3y = 0 and x + y = 16
Since we have 2 linear equations with 2 variables, we COULD solve the system for x, which means we COULD answer the target question
So, statement 2 is SUFFICIENT
Answer: D
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Brent
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x = 10% gravelAAPL wrote:Source: GMAT Prep
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.
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.
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