# Data Sufficiency: The Question Stem - What is the Issue?

If \$\$S\$\$ is a sequence of consecutive multiples of 3, how many multiples of 9 are there in \$\$S\$\$? >(1) There are 15 terms in \$\$S\$\$. >(2) The greatest term of \$\$S\$\$ is 126.
Correct. [[snippet]] For Stat. (1), simulate the problem on a smaller scale of 3 terms: >If \$\$S = \{3, 6, \textbf{9}\}\$\$, then the sequence has only one multiple of 9. >If \$\$S = \{6, \textbf{9}, 12\}\$\$, then there is still only one multiple. >If \$\$S = \{\textbf{9}, 12, 15\}\$\$, then there is still only one multiple. >If \$\$S = \{12, 15, \textbf{18}\}\$\$, then the number 9 is out, but 18 is in, so there is still only one multiple. This little exercise shows that every three multiples of 3 will include one multiple of 9. Therefore, if \$\$S\$\$ includes 15 multiples of 3, then \$\$S\$\$ will include 5 multiples of 9—one for every three terms. Only 1 possible value for the number of multiples of 9 in \$\$S\$\$, so **Stat.(1) → S → AD**. From Stat. (2) alone you do not know the number of consecutive multiples of 3 in the set since this is only stated in Stat. (1). Thus, set \$\$S\$\$ could include 2 consecutive multiples (123 and 126), or 5 consecutive multiples, or 15 multiples, each composition of the set leading to a different number of multiples of 9. **Stat.(2) → IS → A**.
Incorrect. [[snippet]] From Stat. (2) alone you do not know the number of consecutive multiples of 3 in the set since this is only stated in Stat. (1). Thus, set \$\$S\$\$ could include 2 consecutive multiples (123 and 126), or 5 consecutive multiples, or 15 multiples, each composition of the set leading to a different number of multiples of 9. **Stat.(2) → IS**.
Incorrect. [[snippet]] For Stat. (1), simulate the problem on a smaller scale of 3 terms: >If \$\$S = \{3, 6, \textbf{9}\}\$\$, then the sequence has only one multiple of 9. >If \$\$S = \{6, \textbf{9}, 12\}\$\$, then there is still only one multiple. >If \$\$S = \{\textbf{9}, 12, 15\}\$\$, then there is still only one multiple. >If \$\$S = \{12, 15, \textbf{18}\}\$\$, then the number 9 is out, but 18 is in, so there is still only one multiple. This little exercise shows that every three multiples of 3 will include one multiple of 9. Therefore, if \$\$S\$\$ includes 15 multiples of 3, then \$\$S\$\$ will include 5 multiples of 9—one for every three terms. Only 1 possible value for the number of multiples of 9 in \$\$S\$\$, so **Stat.(1) → S → AD**.
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.