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If r, s, t, and u are positive integers such that (r+s)(t+u) is an odd integer and (r+s+t)(s+t+u) is an odd integer, which of the following statements must be true?
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A.s and t are both even
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B.s and t are both odd.
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C.s is even and t is odd.
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D.s is odd and t is even.
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E.s is even if t is odd, and s is odd if t is even.
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