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# Data Sufficiency: Basic Work Order

What is the value of positive integer $$x$$? >(1) $$1 \le x^5 \le 36$$ >(2) $$2x \ne x^2$$
Correct. [[snippet]] According to Stat. (1), $$x$$ can be 1 or 2 because $$1^5 = 1$$, so $$1 \le 1^5 \le 36$$ does satisfy the statement, but >$$2^5 = 2\cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$$, which is also between 1 and 36, so 2 also satisfies the statement. So $$x$$ can have more than one value. No definite answer, so Stat.(1) → IS → BCE. According to Stat. (2), $$2x$$ is not equal to $$x^2$$. The only integer for which this is not true is 2, since $$2 \cdot 2$$ _is_ equal to $$2^2 = 4$$. So Stat. (2) basically tells you that $$x$$ can be any integer other than 2. No definite answer, so Stat.(2) → IS → CE. According to Stat. (1+2), Statement (1) limits the value of $$x$$ to 1 and 2, and Statement (2) eliminates 2 as a possible answer. Using both statements together, $$x=1$$. Definite answer, so, Stat.(1+2) → S → C.
Incorrect. [[snippet]] According to Stat. (2), $$2x$$ is not equal to $$x^2$$. The only integer for which this is not true is 2, since $$2 \cdot 2$$ _is_ equal to $$2^2 = 4$$. So Stat. (2) basically tells you that $$x$$ can be any integer other than 2. No definite answer, so Stat.(2) → IS → ACE.
Incorrect. [[snippet]] According to Stat. (1), $$x$$ can be 1 or 2 because $$1^5 = 1$$, so $$1 \le 1^5 \le 36$$ does satisfy the statement, but >$$2^5 = 2\cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$$, which is also between 1 and 36, so 2 also satisfies the statement. So $$x$$ can have more than one value. No definite answer, so Stat.(1) → IS → BCE.
Incorrect. [[snippet]] According to Stat. (1), $$x$$ can be 1 or 2 because $$1^5 = 1$$, so $$1 \le 1^5 \le 36$$ does satisfy the statement, but >$$2^5 = 2\cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32$$, which is also between 1 and 36, so 2 also satisfies the statement. So $$x$$ can have more than one value. No definite answer, so Stat.(1) → IS → BCE. According to Stat. (2), $$2x$$ is not equal to $$x^2$$. The only integer for which this is not true is 2, since $$2 \cdot 2$$ _is_ equal to $$2^2 = 4$$. So Stat. (2) basically tells you that $$x$$ can be any integer other than 2. No definite answer, so Stat.(2) → IS → CE.
Incorrect. [[snippet]] According to Stat. (1+2), Statement (1) limits the value of $$x$$ to 1 and 2, and Statement (2) eliminates 2 as a possible answer. Using both statements together, $$x=1$$. Definite answer, so, Stat.(1+2) → S → C.
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.