Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements sufficient to answer the question.
There are 4 positive integers (A, B, C and D). What is the value of C?
I. The average of A, B, C and D is 42.
II. `AltBltCltD`. The average of B and C is 40 , A and B are equidistant from 28. A and C are equidistant from 32

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient .to answer the question.
B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
C. if the data 'in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both the statements I and II are not sufficient to answer the question.

Answer

To solve the question, we need to analyze the two statements provided and determine if they are sufficient to find the value of C.

### Step-by-Step Solution:

1. **Understanding the First Statement:**
- The first statement tells us that the average of A, B, C, and D is 42.
- We can express this mathematically:
\[ \frac{A + B + C + D}{4} = 42 \]
- Multiplying both sides by 4 gives:
\[ A + B + C + D = 168 \]
- However, this equation alone does not provide enough information to isolate the value of C, as we have three other variables (A, B, and D) that we do not know.

2. **Understanding the Second Statement:**
- The second statement provides several pieces of information:
- The average of B and C is 40:
\[ \frac{B + C}{2} = 40 \implies B + C = 80 \]
- A and B are equidistant from 28, which implies:
\[ A = 28 - x \quad \text{and} \quad B = 28 + x \]
- A and C are equidistant from 32, which implies:
\[ A = 32 - y \quad \text{and} \quad C = 32 + y \]

3. **Finding Relationships:**
- From the equations derived from the second statement:
- We have two expressions for A: \( A = 28 - x \) and \( A = 32 - y \).
- Setting these equal gives:
\[ 28 - x = 32 - y \implies y = x + 4 \]
- Now substituting \( y \) in the equation for C:
\[ C = 32 + (x + 4) = 36 + x \]

4. **Using the Sum of B and C:**
- We already found that \( B + C = 80 \).
- Substitute \( B = 28 + x \) and \( C = 36 + x \):
\[ (28 + x) + (36 + x) = 80 \]
- Simplifying gives:
\[ 64 + 2x = 80 \implies 2x = 16 \implies x = 8 \]
- Now substituting \( x \) back to find C:
\[ C = 36 + 8 = 44 \]

5. **Conclusion:**
- From the second statement, we have determined that \( C = 44 \).
- The first statement alone was not sufficient to determine the value of C.

### Final Answer:
The value of C is **44**.