Find the sum of all numbers in between 10–50 excluding all those numbers which are divisible by 8. (include 10 and 50 for counting.)

Options

A. 1070
B. 1220
C. 1320
D. 1160

Answer

To solve the problem of finding the sum of all numbers between 10 and 50, excluding those divisible by 8, we will follow these steps:

### Step 1: Identify the range and the numbers
We need to consider all integers from 10 to 50, inclusive. This means we will include both 10 and 50 in our calculations.

### Step 2: Calculate the total sum of numbers from 10 to 50
To find the sum of all integers from 10 to 50, we can use the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2} \times (a + l) \]
Where:
- \(n\) = number of terms
- \(a\) = first term (10)
- \(l\) = last term (50)

First, we need to find \(n\):
\[ n = 50 - 10 + 1 = 41 \]

Now, we can calculate the sum:
\[ S = \frac{41}{2} \times (10 + 50) = \frac{41}{2} \times 60 = 41 \times 30 = 1230 \]

### Step 3: Identify numbers divisible by 8 in the range
Next, we need to find the numbers between 10 and 50 that are divisible by 8. The multiples of 8 in this range are:
- 16
- 24
- 32
- 40
- 48

### Step 4: Calculate the sum of numbers divisible by 8
Now we will sum these numbers:
\[ S_{div\_by\_8} = 16 + 24 + 32 + 40 + 48 \]
Calculating this step by step:
\[ 16 + 24 = 40 \]
\[ 40 + 32 = 72 \]
\[ 72 + 40 = 112 \]
\[ 112 + 48 = 160 \]

### Step 5: Subtract the sum of numbers divisible by 8 from the total sum
Now we will subtract the sum of numbers divisible by 8 from the total sum:
\[ S_{final} = S - S_{div\_by\_8} = 1230 - 160 = 1070 \]

### Final Answer
Thus, the sum of all numbers between 10 and 50, excluding those divisible by 8, is:
\[ \boxed{1070} \]