Based on the numerical analogy given, choose the correct answer from the options given below:
`16 : 56 :: 32 : ?`

Options

A. 112
B. 120
C. 128
D. 96

Answer

To solve the analogy problem `16 : 56 :: 32 : ?`, we can follow these steps:

### Step 1: Set up the proportion
We can express the analogy as a proportion:
\[ \frac{16}{56} = \frac{32}{x} \]

### Step 2: Cross-multiply
To eliminate the fractions, we cross-multiply:
\[ 16 \cdot x = 32 \cdot 56 \]

### Step 3: Calculate the right side
Now, we need to calculate \(32 \cdot 56\):
\[ 32 \cdot 56 = 1792 \]

### Step 4: Substitute back into the equation
Now, we substitute this value back into our equation:
\[ 16x = 1792 \]

### Step 5: Solve for x
To find \(x\), we divide both sides by 16:
\[ x = \frac{1792}{16} \]

### Step 6: Perform the division
Now, we perform the division:
\[ x = 112 \]

### Conclusion
Thus, the answer to the analogy is:
\[ 32 : 112 \]

### Final Answer
The correct answer is \(112\).

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