What is the value of x?

VERITAS PREP OFFICIAL SOLUTION:

C. This problem is a classic example of the "Why Are You Here" strategy. Clearly statement 2 is not sufficient on its own, so why was it written?

In statement 1, the "obvious" answer for x is that x = 2013 and (x + 1) would then equal 2014. Which looks pretty sufficient. But there's one additional, not as obvious possibility: x = -2014 and (x + 1) = -2013. Since negative-times-negative is positive, that would give the same result. So statement 1 looks pretty sufficient but it is not. Statement 2 provides that little clue by emphatically stating that x is odd. That should get you thinking "how could x not be odd?" and of course that would be if x were -2014 and x + 1 were -2013. With both statements together, that negative-negative possibility is off the table, so the correct answer is C.