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
