In each of the following questions , three statements of numbers following same rules are given . Find the rule and accordingly find the value of the number ?
If `1 xx 2 = 32, 4 xx 3 = 712, 4 xx 7 = 1128`, then `5 xx 1 = ?`

Options

A. 63
B. 64
C. 65
D. 66

Explanation

To solve the problem, we need to identify the pattern or rule that applies to the given statements. Let's break down the steps:

### Step 1: Analyze the given statements
1. **1 xx 2 = 32**
2. **4 xx 3 = 712**
3. **4 xx 7 = 1128**

### Step 2: Identify the pattern
From the first statement:
- **1 xx 2 = 32**
- The first part (3) can be obtained by adding 1 and 2: \(1 + 2 = 3\)
- The second part (2) can be obtained by multiplying 1 and 2: \(1 \times 2 = 2\)
- Therefore, we can represent it as: \(1 + 2\) (first digit) and \(1 \times 2\) (second digit) which gives us 32.

From the second statement:
- **4 xx 3 = 712**
- The first part (7) can be obtained by adding 4 and 3: \(4 + 3 = 7\)
- The second part (12) can be obtained by multiplying 4 and 3: \(4 \times 3 = 12\)
- Thus, it can be represented as: \(4 + 3\) (first digit) and \(4 \times 3\) (second digit) which gives us 712.

From the third statement:
- **4 xx 7 = 1128**
- The first part (11) can be obtained by adding 4 and 7: \(4 + 7 = 11\)
- The second part (28) can be obtained by multiplying 4 and 7: \(4 \times 7 = 28\)
- Thus, it can be represented as: \(4 + 7\) (first digit) and \(4 \times 7\) (second digit) which gives us 1128.

### Step 3: Apply the identified rule to find 5 xx 1
Now we need to find the value of **5 xx 1**:
- First part: \(5 + 1 = 6\)
- Second part: \(5 \times 1 = 5\)

So, we combine these results:
- The first part is 6 and the second part is 5, which gives us **65**.

### Final Answer
Thus, the value of **5 xx 1** is **65**.

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