2020 · Q20
If Aₙ = Pₙ + 1, where Pₙ is the product of the first n prime numbers, then consider the following statements:
- 1Aₙ is always a composite number.
- 2Aₙ + 2 is always an odd number.
- 3Aₙ + 1 is always an even number.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- C3 only
- D2 and 3 only
Explanation
P_n is even, so A_n is odd: A_n+1 is even (statement 3 true) and A_n+2 is odd (statement 2 true). But A_1 = 2+1 = 3 is prime, so statement 1 is false. Statements 2 and 3 only - option (D).