# If x & y are odd, w & z is even , then 1/8((x2+y2) * (w2+z2)) is _________ a. even b.odd c.is only a fraction d.none

$we\;know\;that\\*even\times even=even\\*even\times odd=even\\* odd\times even=even\\*odd\times odd=odd\\*As\;we\;know\;that\;x\;and\;y\;are\;odd\;so ,\;x^2\;and\;y^2\;are\;odd\\*and\;w\;and\;z\;are\;even\;so,\;w^2\;and\;z^2\;are\;even\\*Also,\;w\;and\;z\;are\;even\;then\;2\;is\;multiple\;of\;them\;so,\;4\;is\;multiple\;of\\*w^2\;and\;z^2\\*And\;even+odd=odd\\*even+even=even\\*odd+odd=even\\*So,\;x^2+y^2=even\\*w^2+z^2=even\\*so,\;we\;can\;take\;4\;common\;from\;w^2+z^2\;and\;2\;from\;x^2+y^2\\*\Rightarrow x^2+y^2=2\times k_1\\*\Rightarrow w^2+z^2=4\times k_2\\*\Rightarrow \frac{2\times k_1\times 4\times k_2}{8}=k_1\times k_1\\* So,\;we\;can\;not\;tell\;properly\;whether\;it\;is\;even\;or\;odd$

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