2024 · Q27
Consider the following statements:
- 1If 3m³ + 2m² + 5m + nm is not an integer, where m and n are integers, then n is not divisible by m.
- 25(8ᵐ) + 2³m is divisible by 48 for all whole numbers m.
Which of the statements given above is/are correct ?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Statement 1: (3m³ + 2m² + 5m + n)/m = 3m² + 2m + 5 + n/m is a non-integer only when n/m is a non-integer, i.e. m does not divide n — true. Statement 2: at m = 0 (a whole number), 5·8⁰ + 2⁰ = 6, which is not divisible by 48 — false. Only statement 1 is correct: option (a).