帮忙看一道数学题 谢谢~

kobe0024

Jerome wrote each of the integers 1 through 20, inclusive, on a separate index card. He placed the cards in a box, then drew cards one at a time randomly from the box, without returning the cards he had already drawn to the box. in order to ensure that the sum of all the cards he drew was even, how many cards did Jerome have to draw?
A19 B12 C11 D10 E3
答案是B
（不太明白，例如 如果抽了7张奇数 5张偶数，和不是仍然是奇数吗？有点晕。。。）