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The number of 6-digit numbers in which the sum of the digits is divisible by 5 is
- a)180000
- b)540000
- c)5 x 105
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The number of 6-digit numbers in which the sum of the digits is divisi...
x x x x x x
Wavs 9 10 10 10 10 6
0 cannot be filled in the first place. In other four places any digit can be filled. After filling the first five places, the last place can be filled by 0 or 5, 1 or 6, 2 or 7, 3 or 8, 4 or 9 depending upon whether the sum or five digits filled is of the form 5m, 5m + 4, 5m + 3, 5m + 2 or 5m + 1 respectively.
∴ The required number of numbers = 9 x 104 x 2
Wavs 9 10 10 10 10 6
0 cannot be filled in the first place. In other four places any digit can be filled. After filling the first five places, the last place can be filled by 0 or 5, 1 or 6, 2 or 7, 3 or 8, 4 or 9 depending upon whether the sum or five digits filled is of the form 5m, 5m + 4, 5m + 3, 5m + 2 or 5m + 1 respectively.
∴ The required number of numbers = 9 x 104 x 2
Most Upvoted Answer
The number of 6-digit numbers in which the sum of the digits is divisi...
x x x x x x
Wavs 9 10 10 10 10 6
0 cannot be filled in the first place. In other four places any digit can be filled. After filling the first five places, the last place can be filled by 0 or 5, 1 or 6, 2 or 7, 3 or 8, 4 or 9 depending upon whether the sum or five digits filled is of the form 5m, 5m + 4, 5m + 3, 5m + 2 or 5m + 1 respectively.
∴ The required number of numbers = 9 x 104 x 2
Wavs 9 10 10 10 10 6
0 cannot be filled in the first place. In other four places any digit can be filled. After filling the first five places, the last place can be filled by 0 or 5, 1 or 6, 2 or 7, 3 or 8, 4 or 9 depending upon whether the sum or five digits filled is of the form 5m, 5m + 4, 5m + 3, 5m + 2 or 5m + 1 respectively.
∴ The required number of numbers = 9 x 104 x 2
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Community Answer
The number of 6-digit numbers in which the sum of the digits is divisi...
Let's break down the problem step by step:
Step 1: Understanding the problem
We are given that we need to find the number of 6-digit numbers in which the sum of the digits is divisible by 5.
Step 2: Analyzing the digits
Since we are dealing with 6-digit numbers, each digit can take values from 0 to 9. Let's analyze the possible values for each digit and their effect on the sum of the digits:
- If the digit is 0, it does not contribute to the sum.
- If the digit is 1, 2, 3, or 4, adding it to the sum will not change its divisibility by 5.
- If the digit is 5, it does not contribute to the sum since it is divisible by 5.
- If the digit is 6, 7, 8, or 9, adding it to the sum will increase its divisibility by 5 by 1.
Step 3: Counting the possibilities
Now, let's count the number of possibilities for each digit position:
- For the first digit position, any digit from 1 to 9 can be chosen (9 possibilities).
- For the second to fifth digit positions, any digit from 0 to 9 can be chosen (10 possibilities each).
- For the sixth digit position, any digit from 0 to 4 can be chosen (5 possibilities).
Step 4: Calculating the total number of possibilities
To calculate the total number of possibilities, we need to multiply the number of possibilities for each digit position together:
Total number of possibilities = 9 * 10 * 10 * 10 * 10 * 5 = 450,000
Step 5: Checking the options
Among the given options, option A is the closest to the calculated total number of possibilities (450,000). Therefore, the correct answer is option A, 180,000.
So, the number of 6-digit numbers in which the sum of the digits is divisible by 5 is 180,000.
Step 1: Understanding the problem
We are given that we need to find the number of 6-digit numbers in which the sum of the digits is divisible by 5.
Step 2: Analyzing the digits
Since we are dealing with 6-digit numbers, each digit can take values from 0 to 9. Let's analyze the possible values for each digit and their effect on the sum of the digits:
- If the digit is 0, it does not contribute to the sum.
- If the digit is 1, 2, 3, or 4, adding it to the sum will not change its divisibility by 5.
- If the digit is 5, it does not contribute to the sum since it is divisible by 5.
- If the digit is 6, 7, 8, or 9, adding it to the sum will increase its divisibility by 5 by 1.
Step 3: Counting the possibilities
Now, let's count the number of possibilities for each digit position:
- For the first digit position, any digit from 1 to 9 can be chosen (9 possibilities).
- For the second to fifth digit positions, any digit from 0 to 9 can be chosen (10 possibilities each).
- For the sixth digit position, any digit from 0 to 4 can be chosen (5 possibilities).
Step 4: Calculating the total number of possibilities
To calculate the total number of possibilities, we need to multiply the number of possibilities for each digit position together:
Total number of possibilities = 9 * 10 * 10 * 10 * 10 * 5 = 450,000
Step 5: Checking the options
Among the given options, option A is the closest to the calculated total number of possibilities (450,000). Therefore, the correct answer is option A, 180,000.
So, the number of 6-digit numbers in which the sum of the digits is divisible by 5 is 180,000.
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