How many natural numbers between 15 and 85 are divisible by 7?
A. 9
B. 10
C. 8
D. 7

Options

A. C
B. A
C. B
D. D

Answer

To find how many natural numbers between 15 and 85 are divisible by 7, we can follow these steps:

### Step 1: Identify the range
We need to find natural numbers that are greater than 15 and less than 85.

### Step 2: Find the first multiple of 7 greater than 15
To find the first multiple of 7 that is greater than 15, we can divide 15 by 7 and round up to the nearest whole number:
- \( 15 \div 7 \approx 2.14 \) (round up to 3)
- The first multiple of 7 is \( 7 \times 3 = 21 \).

### Step 3: Find the last multiple of 7 less than 85
Next, we find the largest multiple of 7 that is less than 85:
- \( 85 \div 7 \approx 12.14 \) (round down to 12)
- The last multiple of 7 is \( 7 \times 12 = 84 \).

### Step 4: List the multiples of 7 between 21 and 84
Now we can list the multiples of 7 from 21 to 84:
- 21, 28, 35, 42, 49, 56, 63, 70, 77, 84.

### Step 5: Count the multiples
Now, we count the numbers in the list:
- There are 10 numbers: 21, 28, 35, 42, 49, 56, 63, 70, 77, 84.

### Conclusion
Thus, the total number of natural numbers between 15 and 85 that are divisible by 7 is **10**.

### Answer
The correct option is **B. 10**.

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