A number when divided by 49 leaves 32 as remainder. This number when divided by 7 will have the remainder as

Options

A. 4
B. 3
C. 2
D. 5

Answer

To solve the problem, we need to find the remainder when a number, which leaves a remainder of 32 when divided by 49, is divided by 7.

### Step-by-Step Solution:

1. **Understand the given information**:
We know that when a certain number \( N \) is divided by 49, it leaves a remainder of 32. This can be mathematically expressed as:
\[ N = 49k + 32 \]
where \( k \) is some integer.

2. **Identify the relationship between 49 and 7**:
Since 49 is a multiple of 7 (specifically, \( 49 = 7 \times 7 \)), we can use this relationship to find the remainder of \( N \) when divided by 7.

3. **Substitute \( N \) into the division by 7**:
We need to find \( N \mod 7 \):
\[ N = 49k + 32 \]
We can simplify this by taking each term modulo 7:
\[ N \mod 7 = (49k \mod 7) + (32 \mod 7) \]

4. **Calculate \( 49k \mod 7 \)**:
Since \( 49 \) is a multiple of \( 7 \):
\[ 49k \mod 7 = 0 \]

5. **Calculate \( 32 \mod 7 \)**:
Now we need to find the remainder when 32 is divided by 7:
\[ 32 \div 7 = 4 \quad \text{(since \( 7 \times 4 = 28 \))} \]
The remainder is:
\[ 32 - 28 = 4 \]
Thus, \( 32 \mod 7 = 4 \).

6. **Combine the results**:
Now, we can combine our results:
\[ N \mod 7 = 0 + 4 = 4 \]

### Conclusion:
The remainder when the number \( N \) is divided by 7 is **4**.