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# Data Sufficiency: Yes/No Basic Technique

Is $$x$$ closer to $$30$$ than to $$60$$? >(1) $$38 - x\gt x - 32$$ >(2) $$|x - 45| \lt 15$$
Correct. [[snippet]] Stat. (1): solve the given inequality: >$$38 - x\gt x - 32$$ >$$70\gt 2x$$ >$$35\gt x$$ Given that $$x$$ is less than 35, it is closer to 30 than 60. This is a definite answer, so **Stat.(1) → S → AD**. Stat. (2): solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value brackets and solve: >>$$x - 45 \lt 15$$ >>$$x\lt 60$$ 2. Remove the absolute value brackets, put a negative sign around the other side of the inequality, and flip the sign: >>$$x - 45 \gt -15$$ >>$$x \gt 30$$ Based on the above, $$x$$ must be between 30 and 60. That is, $$x$$ can be closer to either 30 or 60. There is no definite answer, so **Stat.(2) → IS → A**.
Incorrect. [[snippet]] Stat. (2): solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value brackets and solve: >>$$x - 45 \lt 15$$ >>$$x\lt 60$$ 2. Remove the absolute value brackets, put a negative sign around the other side of the inequality, and flip the sign: >>$$x - 45 \gt -15$$ >>$$x \gt 30$$ Based on the above, $$x$$ must be between 30 and 60. That is, $$x$$ can be closer to either 30 or 60. There is no definite answer, so **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] Stat. (1): solve the given inequality: >$$38 - x\gt x - 32$$ >$$70\gt 2x$$ >$$35\gt x$$ Given that $$x$$ is less than 35, it is closer to 30 than 60. This is a definite answer, so **Stat.(1) → S → AD**.
Incorrect. [[snippet]] Stat. (2): solve absolute values of the number case by considering two possible scenarios: 1. Copy the inequality without the absolute value brackets and solve: >>$$x - 45 \lt 15$$ >>$$x\lt 60$$ 2. Remove the absolute value brackets, put a negative sign around the other side of the inequality, and flip the sign: >>$$x - 45 \gt -15$$ >>$$x \gt 30$$ Based on the above, $$x$$ must be between 30 and 60. That is, $$x$$ can be closer to either 30 or 60. There is no definite answer, so **Stat.(2) → IS → ACE**.
Incorrect. [[snippet]] Stat. (1): solve the given inequality: >$$38 - x\gt x - 32$$ >$$70\gt 2x$$ >$$35\gt x$$ Given that $$x$$ is less than 35, it is closer to 30 than 60. This is a definite answer, 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.