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# Data Sufficiency: Plugging into Yes/No Data Sufficiency

If \$\$a\$\$ and \$\$b\$\$ are positive integers, is \$\$ab \lt 6\$\$? >(1) \$\$1 \lt a + b \lt 7\$\$ >(2) \$\$ab = a + b\$\$
Incorrect. [[snippet]] Stat (1): If you use \$\$a=1\$\$ and \$\$b=2\$\$, then \$\$ab \lt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 3 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=3\$\$, then \$\$ab = 6\$\$. >\$\$ 1 \lt a+b \lt 7\$\$ >\$\$1 \lt 5 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=4\$\$, then \$\$ab \gt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 6 \lt 7\$\$. No definite answer, so Stat.(1) → IS → BCE.
Correct. [[snippet]] Stat (1): If you use \$\$a=1\$\$ and \$\$b=2\$\$, then \$\$ab \lt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 3 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=3\$\$, then \$\$ab = 6\$\$. >\$\$ 1 \lt a+b \lt 7\$\$ >\$\$1 \lt 5 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=4\$\$, then \$\$ab \gt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 6 \lt 7\$\$. No definite answer, so Stat.(1) → IS → BCE. Stat (2): This statement is >\$\$ab = a + b\$\$. The only possible pair of positive integers that satisfies this equation is \$\$a=2\$\$ and \$\$b=2\$\$: >\$\$(2)(2) = 2 + 2\$\$. Based on this, \$\$ab \lt 6\$\$. Thus, there is a definite answer, so Stat.(2) → S → B.
Incorrect. [[snippet]] Stat (2): This statement is >\$\$ab = a + b\$\$. The only possible pair of positive integers that satisfies this equation is \$\$a=2\$\$ and \$\$b=2\$\$: >\$\$(2)(2) = 2 + 2\$\$. Based on this, \$\$ab \lt 6\$\$. Thus, there is a definite answer, so Stat.(2) → S.
Incorrect. [[snippet]] Stat (1): If you use \$\$a=1\$\$ and \$\$b=2\$\$, then \$\$ab \lt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 3 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=3\$\$, then \$\$ab = 6\$\$. >\$\$ 1 \lt a+b \lt 7\$\$ >\$\$1 \lt 5 \lt 7\$\$. If you use \$\$a=2\$\$ and \$\$b=4\$\$, then \$\$ab \gt 6\$\$. >\$\$1 \lt a + b \lt 7\$\$ >\$\$1 \lt 6 \lt 7\$\$. No definite answer, so Stat.(1) → IS → BCE.
Incorrect. [[snippet]] Stat (2): This statement is >\$\$ab = a + b\$\$. The only possible pair of positive integers that satisfies this equation is \$\$a=2\$\$ and \$\$b=2\$\$: >\$\$(2)(2) = 2 + 2\$\$. Based on this, \$\$ab \lt 6\$\$. Thus, there is a definite answer, so Stat.(2) → S.
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.