Breaking it down in parts to build a suitable equation that describes what is happening:
A Contractor combine x tons of a gravel mixture that contained 10 percent gravel G, by weight,
X tons x 0.1G = X0.1G
with y tons of a micture that contained 2 percent gravel G, by weight,
Y tons x 0.02G = Y0.02G
to produce z tons ofa mixture that was 5 percent gravel G, by weight. What is the value of x?
Z tons x 0.05G = Z0.05G
The complete expression is therefore:
X0.1G + Y0.02G = Z0.05G
We can divide both sides of the equation to disregard G, thus the expression becomes:
X0.1 + 0.02Y = Z0.05 --- (A)
Implied in the question is a constraint that X + Y = Z. Using a logical example, if we add 2 tons of gravel (X) to 3 tons of gravel (Y) we must end up with 5 tons of gravel (Z).
X + Y =Z ---(B)
Using equation (A) and (B) to describe the what is happening we can now evaluate the sufficiency of statement 1.
1) Y= 10
Therefore:
Equation B becomes
X + 10 = Z
Substituting this into equation A we get
0.1X + 0.02(10) = 0.05(X + 10)
We can continue to solve but at this stage one should be able to see that we have a sufficient solution for X. SUFFICIENT
1) z = 16
Equation B becomes
X + Y = 16
Y = 16 - X
Substituting into Equation A we get
0.1X +0.02Y = 0.05(16)
Furthermore Y = 16 - x
0.1X + 0.02(16 - X) = 0.05(16)
Again, we can continue to solve but with one linear equation and one variable it is clear we can arrive at a value for X. SUFFICIENT
Therefore, ANSWER is D. Each statement alone is sufficient.
