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# Data Sufficiency: Plugging into Yes/No Data Sufficiency

Is \$\$a \gt 0\$\$? >(1) \$\$bc \gt 0\$\$ and \$\$ab \lt 0\$\$ >(2) \$\$-b \lt 0\$\$
Incorrect. [[snippet]] According to Stat. (1), >\$\$bc \gt 0\$\$ and \$\$ab \lt 0\$\$. __Plug In__ \$\$b = 2\$\$. Then you can use \$\$c = 3.6\$\$ to satisfy the first inequality. By the second inequality, you get \$\$2a < 0\$\$ and therefore \$\$a \lt 0\$\$, so the answer is "No." But is it always "No"? Try negative numbers: __Plug In__ \$\$b = -4\$\$ and \$\$c = -1.4\$\$. Then \$\$-4a \lt 0\$\$ and therefore \$\$a \gt 0\$\$, so the answer is "Yes." There is no definite answer, so **Stat.(1) → Maybe → IS → BCE**.
Incorrect. [[snippet]] According to Stat. (2), >\$\$-b \lt 0\$\$. Divide both sides by \$\$-1\$\$ to isolate \$\$b\$\$. Don't forget to {color:red}flip{/color} the sign. >\$\$b \gt 0\$\$ That's good to know, but \$\$b \gt 0\$\$ alone tells nothing about the value of \$\$a\$\$. There is no definite answer, so **Stat.(2) → Maybe → IS → ACE**.
Correct. [[snippet]] According to Stat. (1), >\$\$bc \gt 0\$\$ and \$\$ab \lt 0\$\$. __Plug In__ \$\$b = 2\$\$. Then you can use \$\$c = 3.6\$\$ to satisfy the first inequality. By the second inequality, you get \$\$2a < 0\$\$ and therefore \$\$a \lt 0\$\$, so the answer is "No." But is it always "No"? Try negative numbers: __Plug In__ \$\$b = -4\$\$ and \$\$c = -1.4\$\$. Then \$\$-4a \lt 0\$\$ and therefore \$\$a \gt 0\$\$, so the answer is "Yes." There is no definite answer, so **Stat.(1) → Maybe → IS → BCE**. According to Stat. (2), >\$\$-b \lt 0\$\$. Divide both sides by \$\$-1\$\$ to isolate \$\$b\$\$. Don't forget to {color:red}flip{/color} the sign. >\$\$ b \gt 0\$\$ That's good to know, but \$\$b \gt 0\$\$ alone tells us nothing about the value of \$\$a\$\$. There is no definite answer, so **Stat.(2) → Maybe → IS → CE**. According to Stat. (1+2), take a step back and look at what you know: \$\$b\$\$ must be positive. Since we know that \$\$ab\$\$ is negative, it follows that \$\$a\$\$ must be negative. That's a definite "No," so **Stat.(1+2) → Yes → S → C**.
Incorrect. [[snippet]] According to Stat. (1), >\$\$bc \gt 0\$\$ and \$\$ab \lt 0\$\$. __Plug In__ \$\$b = 2\$\$. Then you can use \$\$c = 3.6\$\$ to satisfy the first inequality. By the second inequality, you get \$\$2a < 0\$\$ and therefore \$\$a \lt 0\$\$, so the answer is "No." But is it always "No"? Try negative numbers: __Plug In__ \$\$b = -4\$\$ and \$\$c = -1.4\$\$. Then \$\$-4a \lt 0\$\$ and therefore \$\$a \gt 0\$\$, so the answer is "Yes." There is no definite answer, so **Stat.(1) → Maybe → IS → BCE**. According to Stat. (2), >\$\$-b \lt 0\$\$. Divide both sides by \$\$-1\$\$ to isolate \$\$b\$\$. Don't forget to {color:red}flip{/color} the sign. >\$\$b \gt 0\$\$ That's good to know, but \$\$b \gt 0\$\$ alone tells nothing about the value of \$\$a\$\$. There is no definite answer, so **Stat.(2) → Maybe → IS → CE**.
Incorrect. [[snippet]] Take a step back and look at what you know: \$\$b\$\$ must be positive according to Stat. (2). Since we know that \$\$ab\$\$ is negative, what does that tell you about \$\$a\$\$?
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.