# Quant Fundamentals: Signs and the Number Line

Does $$x+y=x\cdot y$$? >(1) The product of $$x$$ and a positive integer, $$z$$, is not equal to $$x$$. >(2) $$y$$ is neither positive nor negative.
Correct. [[snippet]] For Stat. (1), ignore the third variable, which you know nothing about, and focus on what the question is asking. The variable $$x$$ cannot equal 0, since 0 times anything will still equal 0. Additionally, there is no mention of $$y$$ in this statement, so we can conclude that it is insufficient. **Stat.(1) → Maybe → IS → BCE**. For Stat. (2), the only number that is neither positive nor negative is 0. So $$y$$ equals 0, but does $$x$$ equal 0 as well? We know nothing about $$x$$ from Stat. (2) alone, so $$x$$ could equal 0 as well ("__Yes__") or not equal 0 ("__No__"). There is no definite answer, so **Stat.(2) → Maybe → IS → CE**. For Stat. (1+2), we know that $$y=0$$, so the question is whether $$x= 0$$ as well. However, $$x$$ cannot be 0 because of Stat. (1), which says that if $$x=0$$, then the product of $$x=0$$ with any positive integer $$z$$ will still equal 0, which is equal to $$x$$. Thus, the one value that could've reached an answer of "__Yes__" in the question stem is eliminated, and the answer is a definite "__No__." However, a definite answer of "__No__" is still considered sufficient, so **Stat.(1+2) → No → S → C**.
Incorrect. Did you forget that each statement should be dealt with alone? Remember, _divide and conquer_! [[snippet]] For Stat. (2), the only number that is neither positive nor negative is 0. So $$y$$ equals 0, but does $$x$$ equal 0 as well? We know nothing about $$x$$ from Stat. (2) alone, so $$x$$ could equal 0 as well ("__Yes__") or not equal 0 ("__No__"). There is no definite answer, so **Stat.(2) → Maybe → IS → CE**.
Incorrect. [[snippet]] For Stat. (1), ignore the third variable, which you know nothing about, and focus on what the question is asking. The variable $$x$$ cannot equal 0, since 0 times anything will still equal 0. Additionally, there is no mention of $$y$$ in this statement, so we can conclude that it is insufficient. **Stat.(1) → Maybe → IS → BCE**.
Incorrect. [[snippet]] Neither of the statements is __Sufficient__ on its own. __Plug In__ numbers to prove that this is so.
Incorrect. [[snippet]] According to Stat. (2), $$y$$ must equal 0. Check the question stem: $$x\cdot y=x\cdot 0=0$$ for every value of $$x$$. The only way $$x+0=0$$ is if $$x$$ itself is 0. However, can $$x$$ equal 0 according to Stat. (1)?
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.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.