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# Data Sufficiency: Plugging into Yes/No Data Sufficiency

Is \$\$a \gt b\$\$? >(1) \$\$a \gt c\$\$ >(2) \$\$b\gt c\$\$
Incorrect. [[snippet]] Stat. (1): Plug in values for \$\$a\$\$ and \$\$b\$\$: * If \$\$a = 6\$\$, \$\$b = 4\$\$, and \$\$c = 2\$\$, then \$\$a \gt b\$\$. * If \$\$a = 2\$\$, \$\$b = 3\$\$, and \$\$c = 1\$\$, then \$\$a \lt b\$\$. Thus, \$\$a\$\$ can be greater or less than \$\$b\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] Stat. (2): Plug in values for \$\$a\$\$ and \$\$b\$\$: * If \$\$a = 3\$\$, \$\$b = 5\$\$, and \$\$c = 1\$\$, then \$\$a \lt b\$\$. * If \$\$a = 5\$\$, \$\$b = 3\$\$, and \$\$c = 1\$\$, then \$\$a \gt b\$\$. Thus, \$\$a\$\$ can be greater than or less than \$\$b\$\$. There is no definite answer, so **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] Are you sure that the combination of the two statements is sufficient? All you know is the relation of both \$\$a\$\$ and \$\$b\$\$ to \$\$c\$\$, not the internal relationship between \$\$a\$\$ and \$\$c\$\$.
Incorrect. [[snippet]] Stat. (1): you know nothing about \$\$b\$\$, so \$\$a\$\$ could be both greater than or smaller than \$\$b\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**. Stat. (2): you know nothing about \$\$a\$\$, so \$\$a\$\$ could be both greater than or smaller than \$\$b\$\$. There is no definite answer, so **Stat.(2) → IS → CE**.
Correct. [[snippet]] Stat. (1): you know nothing about \$\$b\$\$, so \$\$a\$\$ could be both greater than or smaller than \$\$b\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**. Stat. (2): you know nothing about \$\$a\$\$, so \$\$a\$\$ could be both greater than or smaller than \$\$b\$\$. There is no definite answer, so **Stat.(2) → IS → CE**. Stat. (1+2): Plug in values for \$\$a\$\$ and \$\$b\$\$: * If \$\$a = b = 2\$\$ and \$\$c = 1\$\$, then \$\$a\$\$ is _not_ greater than \$\$b\$\$, so the answer is "No." * If \$\$a = 3\$\$, \$\$b= 2\$\$, and \$\$c = 1\$\$, then \$\$a\$\$ _is_ greater than \$\$b\$\$, so the answer is "Yes." Thus, \$\$a\$\$ can be greater than or less than \$\$b\$\$. There is no definite answer, so **Stat.(1+2) → IS → E**.
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.