Consider the following statements:<br>1. If (3m^{3}+2m^{2}+5m+n)/m is <strong>NOT</strong> an integer, where m and n are integers, then n is <strong>NOT</strong> divisible by m.<br>2. 5(8^{m})+2^{3m} is divisible by 48 for all whole numbers m.<br>Which of the statements given above is/are correct?
- A. 1 only ✓
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Correct Answer: A. 1 only
Explanation
Statement 1: Expression simplifies to 3m^2+2m+5 + \frac{n}{m}. Since 3m^2+2m+5 is an integer, it fails to be an integer only if n is not divisible by m (True). Statement 2: For m=0, 5(1) + 1 = 6, which is not divisible by 48 (False).
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