Is the positive integer \(m\) divisible by 12? 1. \(m\) is divisible by 6 2. \(m\) is divisible by 8
A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
C. Both Statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient to answer the question.
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Explanation: The question asks: Is \(m\) a multiple of 12? **Statement 1:** \(m\) is divisible by 6. Possible values for \(m\): 6, 12, 18, 24, ... If \(m=6\) or \(18\), the answer is NO. If \(m=12\) or \(24\), the answer is YES. **Not Sufficient.**. **Statement 2:** \(m\) is divisible by 8. Possible values for \(m\): 8, 16, 24, 32, ... If \(m=8\) or \(16\), the answer is NO. If \(m=24\), the answer is YES. **Not Sufficient.**. **Statements 1 and 2 TOGETHER:** \(m\) must be a multiple of both 6 and 8. The least common multiple (LCM) of 6 and 8 is 24. Possible values for \(m\) are multiples of 24: 24, 48, 72, 96, ... Since 12 is a factor of 24, all multiples of 24 are also multiples of 12. Therefore, \(m\) is definitively divisible by 12. **Sufficient.**. The answer is C.
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