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# Data Sufficiency: Yes/No Basic Technique

Is \$\$x \gt 0\$\$? >(1) \$\$|x - 2| \lt 7\$\$ >(2) \$\$x \lt 11\$\$
For Stat. (2), \$\$x\$\$ can have _any_ value less than \$\$11\$\$, that is, it could be positive, zero, or negative. Again, you could use \$\$x=8\$\$ or \$\$x=-3\$\$, so there is no definite answer. **Stat.(2) → IS → CE**. For Stat. (1+2), you know that >\$\$-5 \lt x \lt 9\$\$ and \$\$x < 11\$\$. These inequalities do not conclusively establish whether \$\$x\$\$ is greater than zero or not. Thus, you could still use \$\$x=8\$\$ or \$\$x=-3\$\$, so there is no definite answer. There is no definite answer, so **Stat.(1+2) → IS → E**.
Incorrect. [[snippet]] For Stat. (1), you should solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value signs and solve: >\$\$x - 2 \lt 7\$\$ >\$\$x \lt 9\$\$ 2. Remove the absolute value signs, put a negative sign around the other side of the inequality, and flip the sign: >\$\$x - 2\gt -7\$\$ >\$\$x\gt -5\$\$ Based on the above, \$\$x\$\$ must be more than -5 and less than 9 (i.e., \$\$x\$\$ can be greater or less than 0). Therefore, \$\$x\$\$ could be 8, in which case \$\$x \gt 0\$\$, or -3, in which case \$\$x < 0\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**. For Stat. (2), \$\$x\$\$ can have _any_ value less than 11, that is, it could be positive, zero, or negative. Again, you could use \$\$x=8\$\$ or \$\$x=-3\$\$, so there is no definite answer. **Stat.(2) → IS → CE**.
Incorrect. [[snippet]] For Stat. (1+2), you know that >\$\$-5 \lt x \lt 9\$\$ and \$\$x < 11\$\$. These inequalities do not conclusively establish whether \$\$x\$\$ is greater than zero or not. Thus, you could use \$\$x=8\$\$ or \$\$x=-3\$\$, so there is no definite answer. There is no definite answer, so **Stat.(1+2) → IS → E**.
Incorrect. [[snippet]] For Stat. (1), you should solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value signs and solve: >\$\$x - 2 \lt 7\$\$ >\$\$x \lt 9\$\$ 2. Remove the absolute value signs, put a negative sign around the other side of the inequality, and flip the sign: >\$\$x - 2\gt -7\$\$ >\$\$x\gt -5\$\$ Based on the above, \$\$x\$\$ must be more than -5 and less than 9 (i.e., \$\$x\$\$ can be greater or less than 0). Therefore, \$\$x\$\$ could be 8, in which case \$\$x \gt 0\$\$, or -3, in which case \$\$x < 0\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] For Stat. (2), \$\$x\$\$ can have _any_ value less than \$\$11\$\$, that is, it could be positive, zero, or negative. Thus, you could use \$\$x=8\$\$ or \$\$x=-3\$\$, so there is no definite answer. **Stat.(2) → IS → CE**.
Correct. [[snippet]] For Stat. (1), you should solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value signs and solve: >>\$\$x - 2 \lt 7\$\$ >>\$\$x \lt 9\$\$ 2. Remove the absolute value signs, put a negative sign around the other side of the inequality, and flip the sign: >>\$\$x - 2\gt -7\$\$ >>\$\$x\gt -5\$\$ Based on the above, \$\$x\$\$ must be more than \$\$-5\$\$ and less than \$\$9\$\$ (i.e., \$\$x\$\$ can be greater or less than \$\$0\$\$). Therefore, you could use \$\$x = 8\$\$, in which case \$\$x \gt 0\$\$, or it could be \$\$x = -3\$\$, in which case \$\$x < 0\$\$. There is no definite answer, so **Stat.(1) → IS → BCE**.
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.