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% gravel G, by weight, to produce z tons of a mixture that was 5% gravel G, by weight. What is the value of x?
1. y = 10
2. z = 16
This is a weighted average question: X and Y are being combined to form Z.
We can use alligation, which dictates the following:
The proportion of each element in the mixture is the distance between the percentage attributed to the other element in the mixture and the percentage attributed to the mixture.
Proportion of X = |Percent in Y - Percent in Z| = |2-5| = 3.
Proportion of Y = |Percent in X - Percent in Z| = |10-5| = 5.
X:Y = 3:5.
Since 3+5 = 8, we know that X = 3/8 of the mixture.
Thus, X = (3/8)Z.
Statement 1: Y=10.
Since X:Y = 3:5 = 6:10, X=6.
Sufficient.
Statement 2: Z=16.
Thus, X = (3/8)*16 = 6.
Sufficient.
The correct answer is
D.
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