Practice GMAT Data Sufficiency Question

x is a positive integer; is x + 17,283 odd?

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: A

Before evaluating Statements (1) and (2), it is extremely helpful to keep in mind that an odd number is the result of a sum of numbers with unlike parity. In other words: even + odd = odd. Since 17,283 is odd, the only way x + 17,283 will be odd is if x is even. Consequently, the simplified version of the question is: is x even?
Evaluate Statement (1) alone.
1. Statement (1) says that x - 192,489,358,935 is odd. Since there is only one way for a difference to be odd (i.e., if the parity of the numbers is different), Statement (1) implies that x is even (otherwise, if x were odd, x - 192,489,358,935 would be even). Since Statement (1) gives the parity of x, it is SUFFICIENT.
2. Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
1. Statement (2) says that x/4 is not an even integer. It is important to note that this does not mean that x cannot be even (e.g., 6 is even yet 6/4 is not an even integer). Possible values of x include 2, 3, 6, 10, 11.
  
  x Parity of x x/4
  
  2 Even Not an even integer
  
  3 Odd Not an even integer
  
  6 Even Not an even integer
  
  10 Even Not an even integer
  
  11 Odd Not an even integer
2. As this list indicates, there is no definitive information about the parity of x (e.g., 11 is odd and 10 is even). Consequently, Statement (2) is NOT SUFFICIENT.
3. Statement (2) alone is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, answer A is correct.