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A is sufficient. odd + odd = even. Odd + even = odd. Even + even = even. So if r+t is odd, one of the #'s is odd and one is even. Odd times an even is always even.

B is insufficient. 5^2 is 25, and is odd, and 5*2 is 10, which is even and satisfies the question. But 5^3 is also odd, and 5*3 is 15, which is odd. So you can't tell.

[1] r+t = odd
The only way we can get an odd integer through addition is to add even+odd = odd. Therefore, we know one is even and one is odd, which is sufficient.

[2] r^t = odd
Knowing the rules of multiplication helps here. The only way to get an odd integer through multiplication is odd*odd = odd. So, the only thing this statement tells us is that r is odd. However, we don't know if t is even or odd. Therefore, this is insufficient.

A is sufficient. odd + odd = even. Odd + even = odd. Even + even = even. So if r+t is odd, one of the #'s is odd and one is even. Odd times an even is always even.

B is insufficient. 5^2 is 25, and is odd, and 5*2 is 10, which is even and satisfies the question. But 5^3 is also odd, and 5*3 is 15, which is odd. So you can't tell.