If r, s, and t are nonzero integers, is (r^3)(s^2)(t^4) positive?
1) s is negative
2) rs is negative
1) s is negative
2) rs is negative
Answer is (C). That is both the options together are sufficient for the solution.
In (r^3)(s^2)(t^4), (s^2) and (t^4) will always be positive as they have even powers.
So the solution depends only upon (r^3) and its sign.
r will have same sign as r^3.
Now let's check the options.
1) "s is negative". In this case r can take any sign. So this option is not sufficient.
2) "rs is negative". In this option, either of the r or s is negative. If r is negative(and s is positive) then the expression is negative. But if s is negative(and r is positive) then the expression will be positive. So this statement is not sufficient in giving a unique solution by itself.
1 and 2 combined. "s is negative" and "rs is negative". This means r is positive. Since r is positive, the expression will be positive. So 1 and 2 combined can give a unique solution.
Hence option (C) is correct.
