A number which when divided by 32 leaves a remainder of 29. If this number is divided by 8 the remainder will be

Options

A. 0
B. 1
C. 5
D. 3

Answer

To solve the problem step by step, let's denote the unknown number as \( x \).

### Step 1: Understand the given information
We know that when \( x \) is divided by 32, it leaves a remainder of 29. This can be expressed mathematically as:
\[ x = 32k + 29 \]
for some integer \( k \).

### Step 2: Find the value of \( x \) in terms of \( k \)
From the equation above, we can see that \( x \) can take on multiple values depending on \( k \). However, we don't need the exact value of \( x \); we just need to find the remainder when \( x \) is divided by 8.

### Step 3: Substitute \( x \) into the division by 8
Now we need to find \( x \mod 8 \). We can substitute our expression for \( x \):
\[ x = 32k + 29 \]

### Step 4: Simplify \( x \mod 8 \)
To find \( x \mod 8 \), we can simplify:
1. First, calculate \( 32k \mod 8 \):
\[ 32k \mod 8 = 0 \quad \text{(since 32 is a multiple of 8)} \]
2. Next, calculate \( 29 \mod 8 \):
\[ 29 \div 8 = 3 \quad \text{(which gives a quotient of 3 and a remainder of 5)} \]
Thus,
\[ 29 \mod 8 = 5 \]

### Step 5: Combine results
Now, we can combine the results:
\[ x \mod 8 = (32k \mod 8 + 29 \mod 8) = (0 + 5) = 5 \]

### Conclusion
Therefore, when the number \( x \) is divided by 8, the remainder is:
\[ \boxed{5} \]