Consider the following in respect of prime number p and composite number c.

1.  (p + c)/(p – c) can be even.

2.  2p + c  can be odd.

3.  pc  can be odd.

Which of the statements given above are correct?

(UPSC CSAT – 2023)

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

Solution: (4)

Statement 1.   For p = 11, c = 9,  (p + c)/(p – c) can be even.

Statement 2.   For p =11, c = 9, 2p + c can be odd.

Statement 3.   For p = 11, c = 9, pc  can be odd.

Hence all the statements are correct.