Is $$x$$ percent of $$y$$ greater than $$z$$ percent of $$w$$?
>(1) $$x$$ percent of $$z$$ is one half of $$y$$ percent of $$w$$.
>(2) $$x=y$$ and $$2z=w$$

Correct.
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For Stat. (1), plug in for the variables. If $$x=10$$, $$z=50$$, $$y=10$$, and $$w=100$$, you get an answer of "No."
Ask yourself, is it always "No"? Try different numbers—for instance, $$x=30$$, $$z=20$$, $$y=30$$, and $$w=40$$. The answer is now "Yes." Therefore, **Stat.(1) → Maybe → IS → BCE**.
For Stat. (2), try to use the same numbers if you can to save time and to prevent careless errors. There is no definite answer. Therefore, **Stat.(2) → Maybe → IS → CE**.
For Stat. (1+2), combining the statements does not make any difference, as the numbers prove. Therefore, **Stat.(1+2) → Maybe → IS → E**.

Incorrect.
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For Stat. (1), you can plug in $$x=10$$, $$z=50$$, $$y=10$$, and $$w=100$$ to get a "No"
answer.
Now ask yourself, is it always "No"? Try different numbers—for
instance, $$x=30$$, $$z=20$$, $$y=30$$, and $$w=40$$. The answer is now "Yes." Therefore, **Stat.(1) → Maybe → IS → BCE**.

Incorrect.
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For Stat. (2), you can plug in $$x=10$$, $$z=50$$, $$y=10$$, and $$w=100$$ to get a "No"
answer.
Now ask yourself, is it always "No"? Try different numbers—for
instance, $$x=30$$, $$z=20$$, $$y=30$$, and $$w=40$$. The answer is now "Yes." Therefore, **Stat.(2) → Maybe → IS → ACE**.

Incorrect.
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For Stat. (1+2), you can plug in $$x=10$$, $$z=50$$, $$y=10$$, and $$w=100$$ to get a "No" answer.
Now ask yourself, is it always "No"? Try different numbers—for
instance, $$x=30$$, $$z=20$$, $$y=30$$, and $$w=40$$. The answer is now "Yes."
Combining the statements does not make any difference.

Incorrect.
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For either statement, you can plug in $$x=10$$, $$z=50$$, $$y=10$$, and $$w=100$$ to get a "No" answer.
Now ask yourself, is it always "No"? Try different numbers—for
instance, $$x=30$$, $$z=20$$, $$y=30$$, and $$w=40$$. The answer is now "Yes."

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.