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Data Sufficiency: Plugging into Yes/No Data Sufficiency

Is $$y^{−x}$$ positive? >(1) $$y$$ is positive. >(2) $$x$$ is negative.
Incorrect. [[snippet]] For Stat. (1), as a preliminary step, get rid of the negative exponent: >$$y^{−x} = \frac{1}{y^x}$$. If the base $$y$$ is positive, then $$\frac{1}{y^x}$$ will always be positive regardless of the value of $$x$$. If you're not sure, plug in numbers. Plug in $$y=2$$. * If $$x=3$$, you get $$y^{−x} = \frac{1}{2^3} = \frac{1}{8}$$, which is positive. * Even if you plug in a negative value for $$x$$, such as $$x=-3$$, you get $$y^{−x} = 2^{-(-3)} = 2^3 = 8$$, which is also positive. That's a definite "Yes." **Stat.(1) → Yes → S → AD**.
Incorrect. [[snippet]] For Stat. (2), plug in a positive $$y$$ and a negative $$x$$—for example, $$y=2$$ and $$x=-3$$. >$$y^{-x} = 2^{-(-3)} = 2^3 = 8$$. The number 8 is positive, so that's a "Yes." However, is it always "Yes" for _any_ number? Think of a __DOZEN F__ value for $$y$$, such as $$y=0$$. If $$y=0$$, then >$$y^{-x} = 0^{-(-3)} = 0^3 = 0$$. We know 0 is not positive, so the answer in this case is "No." Therefore, there is no definite answer, so **Stat.(2) → Maybe → IS → ACE**.
For Stat. (2), plug in a positive $$y$$ and a negative $$x$$—for example, $$y=2$$ and $$x=-3$$. >$$y^{-x} = 2^{-(-3)} = 2^3 = 8$$. The number 8 is positive, so that's a "Yes." However, is it always "Yes" for _any_ number? Think of a __DOZEN F__ value for $$y$$, such as $$y=0$$. If $$y=0$$, then >$$y^{-x} = 0^{-(-3)} = 0^3 = 0$$. We know 0 is not positive, so the answer in this case is "No." Therefore, there is no definite answer, so **Stat.(2) → Maybe → IS → A**.
Correct. [[snippet]] For Stat. (1), as a preliminary step, get rid of the negative exponent: >$$y^{−x} = \frac{1}{y^x}$$. If the base $$y$$ is positive, then $$\frac{1}{y^x}$$ will always be positive regardless of the value of $$x$$. If you're not sure, plug in numbers. Plug in $$y=2$$. * If $$x=3$$, you get $$y^{−x} = \frac{1}{2^3} = \frac{1}{8}$$, which is positive. * Even if you plug in a negative value for $$x$$, such as $$x=-3$$, you get $$y^{−x} = 2^{-(-3)} = 2^3 = 8$$, which is also positive. That's a definite "Yes." **Stat.(1) → Yes → S → AD**.
Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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