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# Data Sufficiency: Yes/No Basic Technique

\$\$Q\$\$ is a sequence of consecutive integers. Does \$\$Q\$\$ contain exactly one multiple of 7? >(1) There are at least six integers in \$\$Q\$\$. >(2) There are exactly eight integers in \$\$Q\$\$.
Incorrect. [[snippet]] Stat. (1): __Plug In__ numbers for \$\$Q\$\$ to prove that Stat. (1) is insufficient. If \$\$Q\$\$ has six terms and begins with 7 – making it \$\$\{7, 8, 9, 10, 11, 12\}\$\$ – then it will have only one multiple of 7, yielding an answer of "Yes". However, at least 6 terms also allows the possibility of set \$\$Q\$\$ containing 1,000 terms, and therefore yielding an answer of "No". There is no definite answer, so **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] Stat. (2): __Plug In__ possible numbers for the first term in \$\$Q\$\$. If you plug in 1 for the first term, then it has just _one_ multiple of 7. If you plug in 7 for the first term, then it contains _two_ multiples of 7: 7 and 14. Thus, there is no definite answer, so **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] Stat. (1+2): Stat. (1) does not add new information compared to what is provided by Stat. (2). The number of multiples of 7 in \$\$Q\$\$ still depends on its first term, which is not known. No definite answer can be determined, so **Stat.(1+2) → IS → E**.
Incorrect. [[snippet]] Stat. (1): __Plug In__ numbers for \$\$Q\$\$ to prove that Stat. (1) is insufficient. If \$\$Q\$\$ has six terms and begins with 7 – making it \$\$\{7, 8, 9, 10, 11, 12\}\$\$ – then it will have only one multiple of 7, yielding an answer of "Yes". However, at least 6 terms also allows the possibility of set \$\$Q\$\$ containing 1,000 terms, and therefore yielding an answer of "No". There is no definite answer, so **Stat.(1) → IS → BCE**. Stat. (2): __Plug In__ possible numbers for the first term in \$\$Q\$\$. If you plug in 1 for the first term, then it has just _one_ multiple of 7. If you plug in 7 for the first term, then it contains _two_ multiples of 7: 7 and 14. Thus, there is no definite answer, so **Stat.(2) → IS → CE**.
Correct. [[snippet]] Stat. (1): __Plug In__ numbers for \$\$Q\$\$ to prove that Stat. (1) is insufficient. If \$\$Q\$\$ has six terms and begins with 7 – making it \$\$\{7, 8, 9, 10, 11, 12\}\$\$ – then it will have only one multiple of 7, yielding an answer of "Yes". However, at least 6 terms also allows the possibility of set \$\$Q\$\$ containing 1,000 terms, and therefore yielding an answer of "No". There is no definite answer, so **Stat.(1) → IS → BCE**. Stat. (2): __Plug In__ possible numbers for the first term in \$\$Q\$\$. If you plug in 1 for the first term, then it has just _one_ multiple of 7. If you plug in 7 for the first term, then it contains _two_ multiples of 7: 7 and 14. Thus, there is no definite answer, so **Stat.(2) → IS → CE**. Stat. (1+2): Stat. (1) does not add new information compared to what is provided by Stat. (2). The number of multiples of 7 in \$\$Q\$\$ still depends on its first term, which is not known. No definite answer can be determined, 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.