The number of numbers of 7 digits whose sum of digits is even, is

Options

A. 9000000
B. 4500000
C. 8100000
D. none of these

Answer

To find the number of 7-digit numbers whose sum of digits is even, we can follow these steps:

### Step 1: Determine the range of 7-digit numbers
The smallest 7-digit number is 1,000,000 and the largest is 9,999,999.

### Step 2: Calculate the total number of 7-digit numbers
The total number of 7-digit numbers can be calculated as:
\[ \text{Total 7-digit numbers} = \text{Largest 7-digit number} - \text{Smallest 7-digit number} + 1 \]
Substituting the values:
\[ \text{Total 7-digit numbers} = 9,999,999 - 1,000,000 + 1 = 9,000,000 \]

### Step 3: Determine the distribution of sums
The sum of the digits of these numbers can either be even or odd. Since every alternate number will have an even or odd sum, we can conclude that the numbers are evenly distributed.

### Step 4: Calculate the number of 7-digit numbers with an even sum of digits
Since the total number of 7-digit numbers is 9,000,000, we can find the number of 7-digit numbers with an even sum of digits by dividing the total by 2:
\[ \text{Numbers with even sum of digits} = \frac{9,000,000}{2} = 4,500,000 \]

### Conclusion
Thus, the number of 7-digit numbers whose sum of digits is even is:
\[ \text{Answer} = 4,500,000 \]

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