A contractor combined \(x\) tons of a gravel mixture that contained \(10\) percent gravel \(G,\) by weight, with y tons

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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) \(z = 16\)

Answer: D

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Gmat_mission wrote:
Sun Sep 12, 2021 8:33 am
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) \(z = 16\)

Answer: D

Source: GMAT Prep
Let's use some weighted averages to solve this question
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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