jasmine95

if the sum of five integers is an even integer what is the greatest number of these that can be odd ??
zero
one
two
four
five


i chose five because the rule says if both are even or both are odd so it equal to an even number but the answer is four can anyone help

WiseGuy

Two odd numbers sum to an even number (i.e. 9+9=18, 5+3=8). So four odd numbers (two pairs of two odd numbers) would also sum to an even number (because that is the sum of two even numbers, each coming from the previous set of odd numbers, i.e. 18+8=26). The only way to keep that answer even would be to add another even number, as an even + an odd would give you an odd number. So you can only have four odd numbers.