State whether the following statement is true or false.
If n1,n2,...,np are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.
True
False
A
False
B
True
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Solution
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We know that odd+odd=even.
Consider the sum of n1n2..nn positive integers. Then we can divide the sum as "sum of odd integer plus the sum of even integers". The sum of even integers will always be even.
Hence the total sum will be even if the sum of odd integers is even. That is there are even number of odd integers.
And the total sum will be odd if there are odd number of odd integers. Hence the answer is False.
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