n1 , n2,..., np are p positive integers, whose sum is an even number, then the number of odd integers among them is odd

Question

n1 , n2,..., np are p positive integers, whose sum is an even number, then the number of odd integers among them is odd (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Since, n1 , n2,..., np are p positive integers, whose sum is even and we know that , sum of any two odd integers is even. ∴ Number of odd integers must be even. Hence, it is a false statement.

Q. $n_{1}, n_{2}, ..., n_{p}$ are $p$ positive integers, whose sum is an even number, then the number of odd integers among them is odd

Since, $n_{1}, n_{2}, ..., n_{p}$ are p positive integers, whose sum is even and we know that , sum of any two odd integers is even.
$∴$ Number of odd integers must be even.
Hence, it is a false statement.

Q. n1​,n2​,...,np​ are p positive integers, whose sum is an even number, then the number of odd integers among them is odd

Since, n1​,n2​,...,np​ are p positive integers, whose sum is even and we know that , sum of any two odd integers is even. ∴ Number of odd integers must be even. Hence, it is a false statement.

Q. $n_{1}, n_{2}, ..., n_{p}$ are $p$ positive integers, whose sum is an even number, then the number of odd integers among them is odd

Since, $n_{1}, n_{2}, ..., n_{p}$ are p positive integers, whose sum is even and we know that , sum of any two odd integers is even.
$∴$ Number of odd integers must be even.
Hence, it is a false statement.