A number when divided by 119 leaves remained 19 . If the same number is divided by 17 , the remainder will be

Options

A. 12
B. 10
C. 7
D. 2

Answer

To solve the problem step by step, we need to find the remainder when a number that leaves a remainder of 19 when divided by 119 is divided by 17.

### Step 1: Understand the problem
We know that when a number \( N \) is divided by 119, it leaves a remainder of 19. This can be expressed mathematically as:
\[ N = 119k + 19 \]
where \( k \) is some integer (the quotient).

### Step 2: Substitute values
To find the remainder when \( N \) is divided by 17, we can substitute the expression for \( N \):
\[ N = 119k + 19 \]

### Step 3: Find \( N \mod 17 \)
We need to calculate \( N \mod 17 \):
\[ N \mod 17 = (119k + 19) \mod 17 \]

### Step 4: Calculate \( 119 \mod 17 \)
First, we need to find \( 119 \mod 17 \):
\[ 119 \div 17 = 7 \quad \text{(since } 17 \times 7 = 119\text{)} \]
Thus,
\[ 119 \mod 17 = 0 \]

### Step 5: Calculate \( 19 \mod 17 \)
Now we calculate \( 19 \mod 17 \):
\[ 19 \div 17 = 1 \quad \text{(since } 17 \times 1 = 17\text{)} \]
Thus,
\[ 19 \mod 17 = 2 \]

### Step 6: Combine results
Now we can substitute back into our equation:
\[ N \mod 17 = (119k \mod 17 + 19 \mod 17) \]
Since \( 119k \mod 17 = 0 \):
\[ N \mod 17 = 0 + 2 = 2 \]

### Conclusion
Therefore, when the number \( N \) is divided by 17, the remainder is **2**.