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# Quant Fundamentals: Absolute Value

What is the value of integer \$\$a\$\$? >(1) \$\$1 \le a^3 \le 54\$\$ >(2) \$\$|3a| = a^2\$\$
Incorrect. [[snippet]] According to Stat. (1), \$\$a\$\$ can be 1, 2, or 3: * If \$\$a=1\$\$, then \$\$a^3 = 1\$\$, which is between 1 and 54. * If \$\$a=2\$\$, then \$\$a^3 = 8\$\$, which is between 1 and 54. * If \$\$a=3\$\$, then \$\$a^3 = 27\$\$, which is between 1 and 54. The next number, \$\$a = 4\$\$, results in \$\$a^3 = 64\$\$, which is outside of the scope of the statement. However, we already know that \$\$a\$\$ can have more than one value. There is no definite answer, so **Stat.(1) → IS → BCE**.
Incorrect. [[snippet]] According to Stat. (2), \$\$a\$\$ can be 3, -3, or 0: * If \$\$a=3\$\$, then \$\$|3a| = |9| = 9\$\$ . * If \$\$a=-3\$\$, then \$\$|3a| = |{-9}| = 9\$\$. * If \$\$a=0\$\$, then \$\$|3a| = |0| = 0\$\$. Thus, \$\$a\$\$ can have more than one value, so **Stat.(2) → IS → ACE**.
Correct. [[snippet]] According to Stat. (1), \$\$a\$\$ can be 1, 2, or 3: * If \$\$a=1\$\$, then \$\$a^3 = 1\$\$, which is between 1 and 54. * If \$\$a=2\$\$, then \$\$a^3 = 8\$\$, which is between 1 and 54. * If \$\$a=3\$\$, then \$\$a^3 = 27\$\$, which is between 1 and 54. The next number, \$\$a = 4\$\$, results in \$\$a^3 = 64\$\$, which is outside of the scope of the statement. However, we already know that \$\$a\$\$ can have more than one value. There is no definite answer, so **Stat.(1) → IS → BCE**. According to Stat. (2), \$\$a\$\$ can be 3, -3, or 0: * If \$\$a=3\$\$, then \$\$|3a| = |9| = 9\$\$ . * If \$\$a=-3\$\$, then \$\$|3a| = |{-9}| = 9\$\$. * If \$\$a=0\$\$, then \$\$|3a| = |0| = 0\$\$. Thus, \$\$a\$\$ can have more than one value, so **Stat.(2) → IS → CE**. According to Stat. (1+2), we know Stat. (1) limits the value of \$\$a\$\$ to 1, 2, and 3, and Stat. (2) limits the value of \$\$a\$\$ to 3, -3, or 0. The only value that satisfies both statements is \$\$a = 3\$\$. That is a definite answer, so **Stat.(1+2) → S → C**.
Incorrect. [[snippet]] According to Stat. (1+2), we know Stat. (1) limits the value of \$\$a\$\$ to 1, 2, and 3, and Stat. (2) limits the value of \$\$a\$\$ to 3, -3, or 0. Which of these values satisfy both statements?
Incorrect. [[snippet]] According to Stat. (1), \$\$a\$\$ can be 1, 2, or 3: * If \$\$a=1\$\$, then \$\$a^3 = 1\$\$, which is between 1 and 54. * If \$\$a=2\$\$, then \$\$a^3 = 8\$\$, which is between 1 and 54. * If \$\$a=3\$\$, then \$\$a^3 = 27\$\$, which is between 1 and 54. The next number, \$\$a = 4\$\$, results in \$\$a^3 = 64\$\$, which is outside of the scope of the statement. However, we already know that \$\$a\$\$ can have more than one value. There is no definite answer, so **Stat.(1) → IS → BCE**. According to Stat. (2), \$\$a\$\$ can be 3, -3, or 0: * If \$\$a=3\$\$, then \$\$|3a| = |9| = 9\$\$ . * If \$\$a=-3\$\$, then \$\$|3a| = |{-9}| = 9\$\$. * If \$\$a=0\$\$, then \$\$|3a| = |0| = 0\$\$. Thus, \$\$a\$\$ can have more than one value, so **Stat.(2) → IS → CE**.
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.