What is the value of `x^2 + y+z ?`
I. `4x + 3y+5z=60,2x=y,2y=z`
II.`3x+3y+2z=34, 2x+5y+6z=72`

Options

A. If the Statement I alone is sufficient to answer the question but the Statement II alone is not sufficient
B. If the Statement II alone is sufficient to answer the question but the Statement alone is not sufficient
C. If both Statements I and II together are needed to answer the question
D. If either the Statement I alone or Statement II alone is sufficient to answer the question

Answer

To find the value of \( x^2 + y + z \), we will analyze the two statements provided.

### Step 1: Analyze Statement I
The first statement gives us three equations:
1. \( 4x + 3y + 5z = 60 \)
2. \( 2x = y \)
3. \( 2y = z \)

From the second equation, we can express \( y \) in terms of \( x \):
\[ y = 2x \]

From the third equation, we can express \( z \) in terms of \( y \):
\[ z = 2y = 2(2x) = 4x \]

Now, substitute \( y \) and \( z \) back into the first equation:
\[ 4x + 3(2x) + 5(4x) = 60 \]
This simplifies to:
\[ 4x + 6x + 20x = 60 \]
Combining like terms gives:
\[ 30x = 60 \]
Dividing both sides by 30:
\[ x = 2 \]

Now, substitute \( x \) back to find \( y \) and \( z \):
\[ y = 2x = 2(2) = 4 \]
\[ z = 4x = 4(2) = 8 \]

Now we can find \( x^2 + y + z \):
\[ x^2 + y + z = 2^2 + 4 + 8 = 4 + 4 + 8 = 16 \]

### Step 2: Analyze Statement II
The second statement gives us:
1. \( 3x + 3y + 2z = 34 \)
2. \( 2x + 5y + 6z = 72 \)

We can use the elimination method to solve these equations, but we need to check if we can express \( x^2 + y + z \) directly from these equations.

From the first equation, we can express \( z \):
\[ 2z = 34 - 3x - 3y \implies z = 17 - \frac{3}{2}x - \frac{3}{2}y \]

Substituting \( z \) into the second equation:
\[ 2x + 5y + 6(17 - \frac{3}{2}x - \frac{3}{2}y) = 72 \]
This leads to a complex equation that may not directly give us the values of \( x, y, z \) without further manipulation. Therefore, we cannot directly find \( x^2 + y + z \) from this statement alone.

### Conclusion
From Statement I, we found that \( x^2 + y + z = 16 \). However, Statement II does not provide sufficient information to find \( x^2 + y + z \).

Thus, the answer is that **Statement I alone is sufficient**, while **Statement II alone is not sufficient**.

### Final Answer
The answer is option A: Statement I alone is sufficient, but Statement II alone is not sufficient.