A certain number when divided by 899 leaves the remainder 65. When the same number is divided by 31, the remainder is :

Options

A. 2
B. 3
C. 4
D. 1

Answer

To solve the problem step by step, we need to find the remainder when a certain number, which leaves a remainder of 65 when divided by 899, is divided by 31.

### Step 1: Understand the given information
We are given that when a certain number \( N \) is divided by 899, it leaves a remainder of 65. This can be expressed mathematically as:
\[ N = 899k + 65 \]
for some integer \( k \).

### Step 2: Find the relationship with the second divisor
Next, we need to find the remainder when this number \( N \) is divided by 31. Since we know \( N \) in terms of 899, we can simplify our calculations by focusing on the remainder of 65 when divided by 31.

### Step 3: Calculate \( 65 \mod 31 \)
Now, we need to calculate the remainder when 65 is divided by 31:
\[ 65 \div 31 = 2 \quad \text{(since } 31 \times 2 = 62\text{)} \]
Now, we find the remainder:
\[ 65 - 62 = 3 \]

### Step 4: Conclusion
Thus, the remainder when the number \( N \) is divided by 31 is:
\[ \text{Remainder} = 3 \]

### Final Answer
Therefore, the remainder when the same number is divided by 31 is **3**.

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