If it is known that x, y and z are distinct natural numbers then what is the value of 16x+4y+8z?
Statement I: 3x+y+2z = 22
Statement II: 14x+3y+6z = 96

If it is known that x, y and z are distinct natural numbers then what is the value of 16x+4y+8z? 
Statement I: 3x+y+2z = 22
Statement II: 14x+3y+6z = 96

In statement I, it is given that 3x+y+2z = 22. There are multiple triplets of x, y and z for which this statement is true. Hence, we can uniquely determine the value of 16x+4y+8z.
In statement I, it is given that 14x+3y+6z = 92. There are multiple triplets of x, y and z for which this statement is true. Hence, we can uniquely determine the value of 16x+4y+8z.
By using statement (1)  and (2) : 

3x+y+2z = 22 ... (1)
14x+3y+6z = 92 ... (2)

By substituting (2) - 3*(1), we get

14x+3y+6z - 3*(3x+y+2z) = 96 - 3*22
5x = 30 => x = 6. Also, y + 2z = 4.
We are given that both y and z are distinct natural number. Hence, we can say that y = 2 and z = 1. Now that we have unique value of x, y and z, we can find out the value of 16x+4y+8z. Hence, we can say that this question can be answered using both the statements together. Therfore, option C is the correct answer.