If (x + 1) times (2x + 3) is an odd integer, then x must be:  Choose the correct choice from the following options.
A) an odd integer
B) an even integer
C) a prime number
D) a composite number
E) a negative integer
Solution:   (x + 1) times (2x + 3) means (x + 1)(2x + 3)   (x + 1)(2x + 3) = 2x^2+5x+3   For 2x^2+5x+3 to be odd, 5x+3 must be odd since 2x^2 is always even.   So 5x must be even, hence x must be even.   Therefore x is an even integer.   Answer: an even integer
<result>B</result>
If (x + 1) times (2x + 3) is an odd integer, then x must be: