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# Data Sufficiency: Yes/No Basic Technique

Is $${({4}^{x})}^{5-3x}=1$$? >(1) $$x$$ is an integer. >(2) The product of $$x$$ and positive integer $$y$$ is not $$x$$.
Incorrect. [[snippet]] Stat. (2) is wordy, but what it really means is that $$x\ne 0$$. When 0 is multiplied by any number, the result is always 0; if $$x$$ were 0, then $$x\cdot y$$ would equal $$x$$. According to the statement, $$x\cdot y\ne x$$, so $$x$$ can't be 0. So the only information supplied by this statement alone is that $$x$$ can equal any number except 0. As mentioned above, the answer to the question is only "__Yes__" if $$x=0$$ or $$x=\frac{5}{3}$$ (since only then the exponent equals 0). The variable $$x$$ cannot be 0, but it can still be $$\frac{5}{3}$$, so this statement allows a '"__Yes__" answer. Any other $$x$$ value would result in a "__No__" answer. Therefore, this statement is not sufficient. **Stat.(2) → IS → ACE**.
Stat. (2) is wordy, but what it really means is that $$x\ne 0$$. When 0 is multiplied by any number, the result is always 0; if $$x$$ were 0, then $$x\cdot y$$ would equal $$x$$. According to the statement, $$x\cdot y\ne x$$, so $$x$$ can't be 0. So the only information supplied by this statement alone is that $$x$$ can equal any number except 0. As mentioned above, the answer to the question is only "__Yes__" if $$x=0$$ or $$x=\frac{5}{3}$$ (since only then the exponent equals 0). The variable $$x$$ cannot be 0, but it can still be $$\frac{5}{3}$$, so this statement allows a '"__Yes__" answer. Any other $$x$$ value would result in a "__No__" answer. Therefore, this statement is not sufficient. **Stat.(2) → IS → CE**. According to Stat. (1+2), $$x$$ cannot be 0 or $$\frac{5}{3}$$ (since $$x$$ is an integer). Since these are the only two values that will create a 0 exponent, the definite answer is "__No__." **Stat.(1+2) → S → C**.
Incorrect. [[snippet]] For Stat. (1), if $$x=0$$, then the answer is "__Yes__." However, if $$x=2$$, then the expression will definitely not equal 1, and the answer is "__No__." **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] For Stat. (1), if $$x=0$$, then the answer is "__Yes__." However, if $$x=2$$, then the expression will definitely not equal 1, and the answer is "__No__." **Stat.(1) → IS → BCE**. Stat. (2) is wordy, but what it really means is that $$x\ne 0$$. When 0 is multiplied by any number, the result is always 0; if $$x$$ were 0, then $$x\cdot y$$ would equal $$x$$. According to the statement, $$x\cdot y\ne x$$, so $$x$$ can't be 0. So the only information supplied by this statement alone is that $$x$$ can equal any number except 0. As mentioned above, the answer to the question is only "__Yes__" if $$x=0$$ or $$x=\frac{5}{3}$$ (since only then the exponent equals 0). The variable $$x$$ cannot be 0, but it can still be $$\frac{5}{3}$$, so this statement allows a '"__Yes__" answer. Any other $$x$$ value would result in a "__No__" answer. Therefore, this statement is not sufficient. **Stat.(2) → IS → CE**.
Incorrect. [[snippet]] Remember, in Yes/No Data Sufficiency questions, a definite "__No__" is still considered __Sufficient__.
Correct. [[snippet]] For Stat. (1), if $$x=0$$, then the answer is "__Yes__." However, if $$x=2$$, then the expression will definitely not equal 1, and the answer is "__No__." **Stat.(1) → IS → BCE**.
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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