The rules are:

EVEN ± EVEN = EVEN
 EVEN ± ODD = ODD
 ODD ± EvEN = ODD
  ODD ± ODD = EVEN

EVEN × EVEN = EVEN
 EVEN × ODD = EVEN
 ODD × EVEN = EVEN
  ODD × ODD = ODD


If m and n are odd integers, which of the following must also be an odd integer? 


m is odd, n is odd, 1 is ODD, 2 is EVEN

I. (m + 2)n = (ODD + EVEN) × ODD = ODD × ODD = ODD 
                 
II. (m + 1)(n + 2) = (ODD + ODD)×(ODD + EVEN) = EVEN × ODD = EVEN

III. (m + 2) - n = (ODD + EVEN) - ODD = ODD - ODD = EVEN

Answer:   A  I only

Edwin