How many whole numbers are there between 34 and 242 which are exactly divisible by 6?

Options

A. 35
B. 36
C. 37
D. 38

Answer

To find how many whole numbers are there between 34 and 242 that are exactly divisible by 6, we can follow these steps:

### Step 1: Identify the first whole number greater than 34 that is divisible by 6.
- The first number greater than 34 that is divisible by 6 is 36.

### Step 2: Identify the last whole number less than 242 that is divisible by 6.
- The largest number less than or equal to 242 that is divisible by 6 is 240.

### Step 3: Set up the arithmetic sequence.
- We have an arithmetic sequence where:
- First term (a) = 36
- Last term (l) = 240
- Common difference (d) = 6

### Step 4: Use the formula for the nth term of an arithmetic sequence.
- The nth term of an arithmetic sequence can be calculated using the formula:
\[ l = a + (n - 1) \cdot d \]
Substituting the known values:
\[ 240 = 36 + (n - 1) \cdot 6 \]

### Step 5: Solve for n.
- Rearranging the equation:
\[ 240 - 36 = (n - 1) \cdot 6 \]
\[ 204 = (n - 1) \cdot 6 \]
- Dividing both sides by 6:
\[ n - 1 = \frac{204}{6} = 34 \]
- Therefore:
\[ n = 34 + 1 = 35 \]

### Conclusion:
- There are **35 whole numbers** between 34 and 242 that are exactly divisible by 6.

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