If p is an integer between 1000 and 1030 and if the sum of the digits of p is odd then p must be odd?

Answer 1

If ( p ) is an integer between 1000 and 1030, it can be expressed as ( p = 1000 + n ), where ( n ) ranges from 0 to 30. The sum of the digits of ( p ) is given by ( 1 + \text{(sum of the digits of } n) ). Since 1 is odd, for the total sum of the digits to be odd, the sum of the digits of ( n ) must be even. As a result, if ( p ) is odd, ( n ) must be odd (e.g., 1, 3, 5, etc.), confirming that ( p ) is indeed odd. Thus, the statement is true: if the sum of the digits of ( p ) is odd, then ( p ) must be odd.