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total number of seven digits ,, sum of whose digits is even .. (repitition is allowed)

total number of seven digits ,, sum of whose digits is even .. (repitition is allowed)

Grade:12th pass

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
There are 9000000 seven digit numbers exist.
(because
smallest 7 digit number is 1000000 greatest 7 digit number is 9999999
So total number of 7 digit numbers=9999999 - 1000000+1).
Out of 9000000 numbers 4500000 are having the sum of digits as even and the remaining 4500000 are having the sum of digits as odd.
SinceEvery alternate number has its sum of digits even and odd.
For e.g. Sum of digits in 11 is 2 which is even. Sum of digits of 12 is 3 which is odd. Again sum of digits of 13 is even and that of 14 is odd. There are 9000000 seven digit numbers. So half of it is 4500000
So the required answer is 4500000.
Kushagra Madhukar
askIITians Faculty 629 Points
2 years ago
Dear student,
Please find the answer to your question below.
 
There are 9000000 seven digit numbers exist.
Since smallest 7 digit number is 1000000 greatest 7 digit number is 9999999
So total number of 7 digit numbers = 9999999 – 1000000 + 1.
Out of 9000000 numbers 4500000 are having the sum of digits as even and the remaining 4500000 are having the sum of digits as odd.
Since Every alternate number has its sum of digits even and odd.
For e.g. Sum of digits in 11 is 2 which is even. Sum of digits of 12 is 3 which is odd. Again sum of digits of 13 is even and that of 14 is odd. There are 9000000 seven digit numbers. So half of it is 4500000
So the required answer is 4500000.
 
Hope it helps.
Thanks and regards,
Kushagra
 

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