The remainder is 57 when a number is divided by 10,000. What is the remainder when the same number is divided by 1,000?

Options

A. 5
B. 7
C. 43
D. 57

Answer

To solve the problem, we need to find the remainder when a number, which leaves a remainder of 57 when divided by 10,000, is divided by 1,000.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We know that when a number \( x \) is divided by 10,000, it leaves a remainder of 57. This can be expressed mathematically as:
\[ x = 10,000k + 57 \]
for some integer \( k \).

2. **Dividing by 1,000**:
We need to find the remainder when \( x \) is divided by 1,000. We can substitute the expression for \( x \) from the previous step:
\[ x = 10,000k + 57 \]

3. **Simplifying the Expression**:
Since \( 10,000 \) is a multiple of \( 1,000 \) (specifically, \( 10,000 = 10 \times 1,000 \)), when we divide \( 10,000k \) by \( 1,000 \), it will leave a remainder of 0. Thus, we only need to consider the remainder of \( 57 \) when divided by \( 1,000 \):
\[ x \mod 1,000 = (10,000k + 57) \mod 1,000 \]
This simplifies to:
\[ x \mod 1,000 = (0 + 57) \mod 1,000 \]

4. **Finding the Remainder**:
Therefore, the remainder when \( x \) is divided by \( 1,000 \) is simply:
\[ x \mod 1,000 = 57 \]

### Conclusion:
The remainder when the number is divided by 1,000 is **57**.